Say that Aegon V’s children do not refuse the betrothals he and their mother made for them. Obviously a lot of characters change or disappear, but what do you think might have happened in Westeros history in general?

That’s a really interesting question. 

The first major change is the formation of a royal powerbloc in Westerosi politics – with the Baratheons, Tullys, Redwynes, Tyrells, and whoever else Rhaelle would marry in his corner, plus his Martell relatives, Aegon V would have almost the whole of the South in his corner. This is more sway than many Targaryen kings have had in a  long time.

Two things flow from this immediately: the first is that Aegon’s Reforms (god only knows what they were) are going to go a lot further and get implemented across a broad swathe of Westeros (which makes the holdouts politically isolated), they’re going to last a lot longer (and he’s going to have a lot of tools to deal with the blowback (armies, navies, money, votes in a  Great Council, etc.). The second thing is that Summerhall doesn’t happen, which means the Targaryen dynasty as a whole is going to be a lot more secure, with three princes hopefully siring kids. 

The more long-range possibility is that big events like the Rains of Castamere or the Southron Ambitions conspiracy might get butterflied away entirely – a stronger Aegon V might be able to permanently put a lid on the Reynes short of outright destruction, and without the Baratheons and Tullys, there isn’t much there there to the SAs.