Dear maester Steven, in the event that (after killing Aerys) Jaime learned that Tywin ordered Elia and her children killed and and then he successfully went and protected them, how do you think Robert would have reacted? Do you think that he would have deliberately ordered the royal children killed anyways?

That’s a good question. From what we’ve read, Robert looked relieved that it was done AND that he didn’t have to do it, because murdering children didn’t account for his conception of himself as a hero. 

Certainly, I think Elia would have been gently treated. As Tywin says, by herself she was nothing, and Robert needed goodwill from the Martells as one of the leading loyalist Houses. 

The children…well, Rhaenys you can potentially marry back into the line to consolidate that claim, so that’s less problematic. Aegon’s the problem. The best you can do, short of killing him in such a way that everyone acknowledges he’s dead (because you have to be worried about impostors, given Westerosi history), is have him inducted as a septon and then sent to the Wall, because that’s two holy oaths that disinherit him and it puts him at the edge of the known world right next to the ultra-loyalist Starks.