At a certain point it didn't matter what Victor Emmanuel III wanted as his hands had been effectively cut off by Mussolini politically.

I'm going to preface this to say that the man himself left behind no diaries, and little personal correspondence. When Mussolini came to power he was directly handed it by the Victor Emmanuel after the March on Rome. Mussolini and most of the higher ranking members of the Partito Nazionale Fascista (PNF) were actually quite worried that the King was going to step in and call the Army to crush the rebellion (as future Prime Minister Pietro Badoglio, then a General, told the King that it would be a rout), with Mussolini ready to leave the country. Instead the King decided to let Mussolini come to Rome and handed him power.

This was the prelude to years of Victor Emmanuel turning a blind eye to many of the abuses of both Mussolini personally, and the PNF in general (to include openly assassinating political opponents, and a gradual stripping of democracy from the country). He further did nothing over a period of two years in which Mussolini essentially chopped his balls off and constitutionally tied his hands:

• In January 1925 18 members of the party were appointed to review, and reform the constitution.
• In December 1925 the position of Prime Minister was officially elevated above that of a first among equals position, to one answering to the King and King alone.
• January 1926 Mussolini's decrees were to have the full force of law.
• December 1928 one of the smartest things that Mussolini did was moving the Gran Consiglio del Fascismo from just the highest committee of the party, into an actual organ of the state. The GCF alone would have the power to not just choose the Party Secretary/Prime Minister - taking this power away from the King - but also the King's line of succession. As Mussolini himself retained the right to call the Counsel he had effectively turned himself into a dictator as he controlled what it could, or could not do.

A note on the Gran Consiglio before moving on: prior to 1926 the membership was appointed at the annual meeting of the PNF. After this all members were selected 'from above' with Mussolini remarking that, "I superuomini si elegono" ("Supermen elect themselves.")

What this is suffice to say that unless Mussolini proved himself to be highly unpopular, the King had little legal recourse in which to take him down. With Italians either actively for Mussolini (or repressed into keeping their mouths shut), there was little Victor Emmanuel could do even if he wanted to. Yet.

So to get to part of your question,

So if Mussolini was removed by Emmanuel in 1943, does this mean the King was okay with everything Mussolini had been doing?

Yes. Italian entry into Abyssinia was popular. Italians, fed by Fascist propaganda, were enthusiastically patriotic and in fact openly assaulted Prince Filippo Andrea Doria's (a staunch anti-Fascist) wife for refusing ton contribute her wedding rings to the war cause. The King meanwhile was more than happy to enjoin the spoils of war, gaining the crowns of Ethiopia and Albania in the process. To Victor Emmanuel, a vain man in private and an egotistical man in public, the successes of the Fascists served to illustrate that he made the correct decision in allowing Mussolini to power.

Mussolini himself made it no state secret of what he envisioned Italy's role to play in the 20th Century either (numerous speeches illustrated his desire that the years of 1935-1940 would be when Italy would return to being the 'directing force' for humanity), so even if Victor Emmanuel III had wanted to play coy, that would mean he was willfully ignorant. Instead it is left to assume that he supported what was going on - until the missteps of Mussolini began.

One of the first major missteps that Mussolini took was in the creation of the military rank of primo maresciallo dell'impero (First Marshall of the Empire). The rank was bestowed unto both Mussolini and Victor Emmanuel III, placing them nominally on equal footing as head of the military. Until this point the military (theoretically) belonged to the King, now for the first time in Italian history the royal family shared power with a Prime Minister.

The King was not amused. He saw this as a direct assault on his power, and the first overt signs that Mussolini had designs on getting rid of him. Still, Mussolini and the PNF were still popular - in theory - and he had support of the military. With the constitution amended to the point where the King more or less answered to Mussolini, there wasn't much he could do except express his displeasure.

Or was it an extreme case of overreach where the King wasn't supposed to do it, and said 'fuck it' and overstepped?

After Mussolini's missteps into Albania (which were opposed by the King), the disastrous entry into World War II, it's calamitous experience in the war itself (I talked about it briefly here), and finally with the Allies bombing Rome directly not only had the King had enough, but more importantly the Gran Consiglio del Fascismo had as well.

What happened next saw a series of multiple designs at toppling Mussolini take effect. Both Dino Grandi and Marshal Pietro Badoglio were plotting with (and sometimes without) the King and the military itself had given Mussolini a strict deadline to end the war for Italy and remove itself from Germany's grasp. These plans were all accelerated by the bombing of Rome while Mussolini was in a meeting with Hitler at Feltre on June 19, 1943. A meeting of the Gran Consiglio on the night of July 24-25 saw all plans fall into place: Grandi (who had brought a live grenade with him in the event it was needed) proposed to the council that it recommend to Mussolini that the King resume control as commander of the Armed Forces. With Grandi highlighting that the choice of the council was to prove loyalty to either Mussolini or Italy herself, the council voted in favor of the measure. They also tasked Mussolini with delivering what was in effect a vote of no confidence to the King himself.

This vote of no confidence gave the plotters, and most importantly the King, all the impetus needed to complete their coup. That morning the King met with Badoglio to inform him that he would become the next Prime Minister, and that evening when Mussolini met with Victor Emmanuelle III to present the vote of no confidence the King informed him that it was time to step down. Mussolini is said to have agreed, as his spirits were quite broken at this time. What he was not expecting was that a platoon of Carabinieri were waiting outside to arrest him.

So Constitutionally, no, the King did not over step at all. Mussolini's own council had turned their swords on him and presented the King with the ability to remove him from power.