Vito's comments to Tom seem to me to be very revealing.

By dismissing the possibility that Tattaglia could have been behind Sollozzo, but admitting he didn't know it was Barzini all along, it raises the question of exactly when he realized that there was a "hidden hand" behind Sollozzo/Tattaglia.

The obvious answer is when Santino was outfought. This showed Vito that his true adversary was both hidden and dangerous.

I agree that Vito would have acted differently had he realized this from the start. That's why I believe Vito's sudden determination to end the war was not merely (or even primarily) the act of a grieving father, but that of a Mafia don who realizes he's made a terrible error in judgment.