Well, with the highly significant caveat of Tywin’s “coverup” of who killed them and who gave the order, no. The bodies of the children were publicly displayed, the stories spread far and wide, etc.
Jon Arryn managed to make peace with the Martells, likely by emphasizing the chaos of the Sack of King’s Landing, that none of his own forces participated in the murders in question, and probably emphasizing that, with plenty of Starks murdered in Martell-adjacent locations, the Martells probably didn’t want to open that can of worms when they were so politically isolated.