I think that Michael and Vito purposely gave the impression that Michael was a much weaker man than his father. Even Tessio underestimated him, and Tessio was pretty smart. If even the caporegimes believed that Michael was allowing the other families to muscle in on their territories, why wouldn't Moe Greene believe that they were weak and making the move out to Nevada to start over?

Exactly right SB. And if I might add, I believe that the Corleones really WERE a bit weaker than in the past. Vito and Michael knew this. So while there may have been some truth to their losing SOME power, they used what was partially true to make it appear worse than it was. This bought them some time. It allowed them to re-group, re-build and at the same time see who would remain loyal to them and who would not. It was their way of manipulating this partial truth to their own benfit. Buy some time and then when everything is in place, strike unexpectantly like a thief in the night.
Vito's plan was to train Michael. The more time that he could buy to cultivate Michael, the better it would be in the long run.