I think during that scene "I want no inquiries made", really meant that Vito doesn't have the strength to fight back. Anymore bloodshed would result in more family death members..possibly including himself. With Sonny being gone, there is no one else to lead the war.

That's why Vito had to cave in at the meetings to give the other families their demands so there could be temporary peace.

Since Micheal was hungry for revenge, Vito used that to come up with his flawless plan.