Do you think Jaime would have defended Elia and her children against the Mountain? Or his presence would have not made a difference?
I think the question is somewhat missing the point:
Prince Rhaegar burned with a cold light, now white, now red, now dark. “I left my wife and children in your hands.”
“I never thought he’d hurt them.” Jaime’s sword was burning less brightly now. “I was with the king … [sic]”
Jaime believed in that moment (or convinced himself that he believed - the answer is up to you) that Tywin would not hurt Elia or her children. Jaime likewise knew, as the sack of King's Landing was happening, that Aerys II had refused his, Jaime's, offer to negotiate a surrender and was also meeting with Rossart to conduct the wildfire plan. With no reason to suppose (again, in his own mind, at least) that Elia and the young Targaryens were in any danger, and with the knowledge that it was a question of minutes at most to stop the wildfire plot he alone (apart from the king and his pyromancer co-conspirators) was fully aware of, Jaime had no reason to go and defend Elia and/or her children (especially from an attack he did not know was imminent/already begun - Jaime's memory suggests the scaling of Maegor's Holdfast was happening simultaneously to Jaime killing Rossart and Aerys).
But Tywin did hurt them, of course, and much worse - sending some of his most brutal lieutenants to murder Elia, Rhaenys, and Aegon (and in particularly grisly, violent ways). The fact that Jaime feels a strong sense of guilt over their end is demonstrated by Rhaegar's appearance with this very line in Jaime's dream, as well as the dream-Jaime's reaction to it. The dimming light of Jaime's sword reflects his own guilty memory of the event, shadowed by the knowledge of what had happened: Jaime might answer the ghostly Rhaegar's accusation by citing the more important work of stopping Aerys' last mad act, but he knows that by choosing to be there (i.e. in the throne room to kill Aerys), he denied himself the ability to be elsewhere - that is, with Elia and the children, being killed at virtually the same moment by Tywin's own men.
It's not about whether Jaime would have defended Elia and her children against the Mountain, because that's a scenario that could not have happened. Jaime could not have done differently from what he did and still be Jaime (or this still be the same story) - but that doesn't mean Jaime doesn't know what the alternative was now, and does not mean he does not feel the pain of that choice still.
