It occurs to me that Jaime’s sulky act surrounding his regicide might have less to do with breaking his oath to avert a holocaust than with his own dysfunctional relationship with Tywin. Have we ever seen an account of Tywin’s reaction to Aerys’s death?

I don’t think it’s got a lot to do with his relationship with Tywin – Aerys ordering Jaime to kill his father is the catalyst that gets Jaime to finally act on his feelings, but the feelings that were already there before Tywin enters into it were primarily about the conflict between his romantic conception of knighthood and the horrific reality of serving a mad king who got his rocks off on burning people alive. 

As for Tywin’s reaction to Jaime killing Aerys specifically, I think he would have seen it quite similarly to how he saw the death of Rhaenys and Aegon:

“We had come late to Robert’s cause. It was necessary to demonstrate our loyalty. When I laid those bodies before the throne, no man could doubt that we had forsaken House Targaryen forever.” (ASOS, Tyrion VI)

For Robert to become king, Aerys needed to die. Jaime killing Aerys was another example of the Lannisters demonstrating their loyalty to the new regime, and was thus the necessary and practical thing. 

OTOH, I think Tywin would have felt very differently about what Jaime did after. Sitting the Iron Throne ahead of Robert could have jeopardized the Lannister-Baratheon alliance; if you’re going to sit the throne, you only do it if you mean to rule and have a plan that you’ll ruthlessly pursue to make it happen.

And so on.