Hi there!

This is a bit of a tough one to answer because essentially you're asking a "what-if"? That's fine of course, but it's impossible to cite a source for things that never happened. I can tell you what I think, and I'll back those thoughts up, but someone else could think I was completely wrong- and that would be legitimate. So, I can't answer your question but I can tell you what I think the answer might be.

So, let's say your scenario is correct. The initial reports are true and Titanic, while badly damaged, stays afloat and either limps into New York under her own power or is towed in. What would change?

Honestly? Probably nothing. Why would it? Titanic would have proved, and her sister would have already proved, that they were incredibly safe and could withstand collision and flooding. It would have been a massive success for White Star, slightly embarrassing maybe but if they were able to escape liability for the actual sinking, their PR machine and lawyers could have absolutely spun this as a win.

And they would have been right. You must remember that the Olympic Class Liners were incredibly safe- even if only one survived. Both Titanic and Britannic faced an extraordinary set of circumstances. Olympic encountered far more collision and danger than either of them and simply kept going, retiring to scrap after a long career. Titanic's collision was minor compared to what Olympic went through over the years.

And even then, as I've written before, in a time when ships sank in less than 20 minutes, both sisters held on far longer than anyone thought possible. Titanic took almost 3 hours, Britannic almost an hour. Other liners around the time went down in literal minutes. That's how well designed they were.

So, in reality, another ship surviving another collision would probably just have been more proof that they'd achieved a technological milestone. There might have been some improvements so if it happened again, they weren't so affected, but Titanic would have undergone the same process as her sister- a patch, a fix, and back to work.

That all being said, there are perhaps some regulations that might have still come to pass- at least for the Americans. While the British Inquiry blamed excessive speed (wrong), the American Inquiry decided that-

... this accident clearly indicates the necessity of additional legislation to secure safety of life at sea

So what was that recommended legislation? First on the list- reciprocal regulation. The Senate committee decided that every ship licensed to do business with, enter the borders of, or carry American passengers must- by law- be sailing under the same regulatory standards that their ships were. That means, essentially, if your ship building laws weren't bought up the new-post-Titanic-American-standard, the Senate recommended you not be be allowed to deal with American immigration, passengers, or business.

It is feasible that this may have still come to pass- after all, if we've proven you can't sink our ships, why would you not build them to this standard anyway? So, yes- in this alternate future, I can see that happening with or without the Titanic disaster.

The next would be 24 hour wireless service- which absolutely would have become law eventually even if Titanic hadn't happened. In our fictional scenario- the idea that Titanic could both be reached, towed, and the continents kept up to date of the situation would have guaranteed that the relatively new technology would have proven it's necessity and therefore be regulated to the same standard post reality. Even if Titanic didn't exist at all, that would have happened eventually.

Maybe some small ones, the firing of rockets at sea in a non emergency becoming misdemeanor could be one, but with 24 hour wireless- what difference would it make really? The crew might eventually have tried to unionized at some point without the push of the Titanic disaster to force their hand.

What I highly doubt would have changed were lifeboats and the strict new recommendations and laws governing their use. The reality of the situation is that lifeboats, in many (if not most) cases, had proved pretty useless. Your lifeboat is no good if your ship capsizes and sinks in 14 minutes (Empress of Ireland-1914) or your list is so bad they end up tipping and dumping people into the sea (Lusitania- 1915).

"Titanic didn't have enough lifeboats!" entered the public narrative immediately, and the mandating to increase them was because of that. It didn't matter that more lifeboats wouldn't have done anything to help Titanic's dead, what mattered was message and image. The lifeboat laws were symbolic in a way, that is- they didn't really make a difference but they made people feel better and more comfortable so that was their actual benefit. Sure, it's great to have a seat on a lifeboat for everyone if your ship sinks nice and slowly and calmly and even. That rarely, if ever, happens of course- but if it does- we've got you now!

I'd even go so far to say that, had Titanic survived, lifeboats would have been considered even less of a necessity. Double skins, higher bulkheads- that all could still have come to pass (and it would have anyway), but lifeboats- probably not.

It wasn't ignorance, or hubris, or poetic justice that sent Titanic out unable to safely handle her own sinking- it was bureaucracy. Shipbuilding was moving too quickly and lawmaking was moving too slowly, and they just couldn't keep up with each other until something forced them together.

A lot of what people demanded in response to the Titanic disaster didn't have much to do with how the Titanic disaster unfolded, but was instead reactionary. It wasn't quite on the level of a "seat cushion will float if the plane crashes" placebo, but it wasn't too far off. All the lifeboat laws passed after Titanic made no difference to the three big ships that sank right after her- including her own sister.

As stated above, all in my opinion of course :)

I read through the rules, and this is a "what if'' question. I will answer the question in the title, which is about changes to maritime laws and practices after the Titanic disaster.
First of all there were two inquiries, the American one which happened first and a British one. Many of the immediate changes were not from change in law, but from companies wanting to make their ship safer, but yes, the Safety for life at sea (SOLAS) convention and the formation of the International Ice Patrol (IIP) were founded in 1914. SOLAS 1914 never went into effect because of WWI. So most of what changed immediately was from the shipping lines themselves. For example, White Star added more lifeboats to all of the ships without the law requiring it, changes in law were slow back then, just like today.
Here are the specific changes. Enough Lifeboats and liferafts for every person on board. The formation of the International Ice Patrol. Raising of watertight bulkheads. Reduced speeds in night time conditions. Changes to radio operation, including keeping a 24 hour watch. Rockets at sea would now always mean distress, and never company signals.
Now here is why these changes came about. The adding of lifeboats seems obvious if you only know the common pop culture understanding of the story. The truth is Titanic, even with, by today's standards of it having too few lifeboats, it still did not launch all of the boats. Titanic only successfully launched 18 out of the 20 boats on board, with the other two being floated off, one of them being capsized. The reason they wanted more boats is that survivors recalled seeing people denied lifeboats, never to be seen again, or even being deined themseleves, only to get on another one, or even picked up out of the water by one!
This is partially due to officers incorrectly believing that Titanic's lifeboats could not be lowered at capacity. This is true on other ships, but Titanic's boats were able to do this. Senator Smith, who asked a lot of questions in the American Inquiry, personally saw one of Olympic's lifeboats lowered with 65 people in it after the inquires. For example, 5th Officer Lowe said at the American inquiry "I should not like to put more than 50 in." As well as saying earlier that the capacity of the boats was "65.5". Another thing relating to officer competency was the actions of 2nd Officer Lightoller. He lowered Boat 4 to A deck, forgetting that it was enclosed on the Titanic, unlike the Olympic. This wasted time, as they needed the key to open the windows to get survivors through, and boat 4 was one of the last boats to leave, despite being one of the first to be lowered, even though no one was in it while lowering. He also wasted no less than 10 minutes looking for a non existent plug for Collapsible D. The officers should have known better.
The Ice Patrol is more obvious, as Titanic had been steaming into a known ice region, at speed, in the middle of the night, with only two lookout's in the crows nest looking ahead. Surprisingly, this was actually universal practice at the time, as testified by 11 captains who said such at the inquires, Including Captain Pritchard of the Mauretania, the fastest ship in the world at the time. He said "As long as the weather is clear I always go full speed." The disaster increased the importance of ice warnings, and stopped this practice.
Watertight bulkheads are also fairly obvious. If you are unfamiliar, here is a scene from the movie A Night To Remember, where an actor explains how the ship flooded. There are a couple mistakes, such as there is not a 300 foot gash, but 6 small holes totaling about 12 square feet, or about the size of a doorway. Also, a minor mistake is that, although it is true that the ship could float with the first four compartments flooded, Andrews could not have known this, as the math for that had only been done after the disaster.
The Olympic, Titanic's sister, had her watertight bulkheads raised, 5 of them now going as high as B deck. This allowed her to survive with the forward most 6 compartments flooded, or any 3. She also had other changes such as a double hull added a midship, and ofcourse, far more lifeboats. The youngest of the three, Britannic, also had 5 expansion joints, as opposed to 2 on Titanic. This is speculated to be because White Star believed Titanic possibly broke into pieces when sinking, which was not what the general public believed. For those who do not know, expansion joints allow the superstructure, or the higher parts of the ship, to flex, to prevent damage from larger waves, which would happen on a rigid ship.
The Titanic disaster proved the common practice of maintaining speed deadly, so ice warnings got taken more seriously. It is fairly obvious why, more ships got radios and 24 hour watches, and laws were passed to insure this, such as the radio act of 1912. This required ships to have a radio, and keep watch for distress.
Rockets meaning distress seems obvious as well. This was different in 1912. Rockets fired did not always mean distress, as they were used for company signals. Rockets fired regularly every minute to mean distress. 4th Officer Boxhall fired these at a rate of about one every 5 minutes. This has to do with the Californian controversy, which is very complex. There was a ship, which distance is unknown to Titanic, as little as 8 miles, and as many as 20 miles. She saw the rockets go up, and they just used a morse lamp, a bright light for signaling ships in morse code. Ofcourse, there are many more details to this, but with the new radio system on ships, rockets being signals was outdated. This changed to always mean distress.