Wouldn’t the timing of Robert’s elevation and official crowning be everything in determing the legality of any fealty sworn to him and his successors though? While he put forth his intent to make a claim before the Trident Robery wasn’t officially coronated until King’s Landing. In my own fanfiction Wolf’s Reign I had Robert die before said coronation, so wouldn’t a stickler for the law like Stannis see his own elevation as unlawful and revert to his previous oath to House Targaryen instead?

It’s way more complicated than dating from the coronation ceremony; to give a historical example of how tricky this could get, Henry VII had Parliament declare the beginning of his reign to be the day before the Battle of Bosworth Field, so that he could declare men guilty of treason for supporting Richard III, despite the fact that at the time Richard had been named King of England by Parliament in 1484 and thus was the legal monarch of England. To put a further point to it, Richard III was crowned King on July 6th 1483 but not declared King by Parliament until January of 1484. Similarly, Edward IV proclaimed himself King in March 1461, but wasn’t crowned until the end of June. 

So the coronation isn’t the main legal factor, as we can see from examples where kings inherit the throne from fathers who never held the throne themselves because they died young – Richard II, for example, became King of England despite the fact that his father, Edward the Black Prince, had died before his grandfather King Edward III. 

In this case, Stannis is Robert’s heir, and the oath of fealty would have been sworn to Robert’s heir(s) as well as to Robert personally.