I also just asked this in /r/askhistory but this sub seems a lot more populated.
I'm writing a historical fiction novel that takes place in the years before and at the start of the reign of Shulgi, son of Ur-Nammu. I am trying to go by Middle Chronology, and using good old Wikipedia I can place the beginning of the dynasty at 2112 BCE (2047 short). 17 years later, in 2094 BCE (2030 short) Ur-Nammu dies suddenly in battle with the ousted Gutians and his son Shulgi takes over. I'm having difficulty doing the math here, as it seems like either Shulgi was an infant when his 48-year reign began, or he was possibly 17, or something else entirely. My question is, how old was Shulgi when his father died?
Bonus questions: Is there information on how long it took for Shulgi to come to power, whether it was immediate or took perhaps up to a year (poems indicate social chaos followed Ur-Nammu's death)? Perhaps if there was any sort of contemporary political intrigue that could be drawn upon for dramatic effect?
All of the dates that you mention and that we know are years of rule, not years alive. It is impossible produce anything more than a rough guess for the ages of Sumerian kings based on their reigns. Google's algorithm confuses the start of the reign with his birth, so anything you see that indicates Shulgi's "birth" is a mistake for the start of his reign. This issue is compounded by 1) the fact that there are Sumerian hymns that mention his birth (so reference works citing his years of rule are confused with his "birth" by a keyword algorithm), and 2) the chronology issues, which you already mentioned, confuse non-specialists, leaving only a vague sense of when things started and ended.
When Utu-Hegal (of Uruk) died, Ur-Namma gained control of the region in 2112. Shulgi took over when his father died in 2094. Shulgi reigned a long time (48 years), so he was probably pretty young when he took the throne, but there is no way of knowing how old. His first twenty one years of rule passed relatively quietly so he may have been very young, indeed, when he took the throne, but it seems doubtful to me that he could have been an infant since the dynastic control of the region wasn't that secure yet. I'd reckon he was about 12 if you need a guess, but that's all it is. It's a guess that allows him to live to be 60 years old, which is a standard number for the age of venerable kings in the Bronze Age so it has a certain mytho-literary charm.
As to your bonus question, I am not a specialist of the period, but I have never heard of there being difficulty surrounding Shulgi's succession. Neither Van De Mieroop nor the Cambridge Ancient History mention it so it might just be a literary formula in a royal hymn to make Shulgi's reign seem more triumphant. There doesn't appear to be any historical basis for it.