Michael decided to move the family to Nevada, probably with Vito's blessing. The move was crucial to Michael's long-term goal--obsession--to become "legitimate" by leveraging the Corleones' dominance of gambling and channeling it into legalized gambling. At that time (mid to late '50's), gambling was legalized in only two places in the Western Hemisphere: Nevada and Cuba.
Michael simply decided that he was going to be Numero Uno, and that nothing--not Moe Green, not Klingman, not the Lakeville Road Boys, not Hyman Roth--was going to stop him. He swatted Moe like a fly, and Roth accepted it. He could easily have swatted Klingman, the Lakeville Road Boys, and anyone else in Nevada, too. But he chose to curry favor with Roth, because Roth controlled gaming in the other place Michael wanted for his empire: Havana. So, in the deal he and Roth ostensibly agreed to, he'd become Roth's heir-apparent in Havana, and agree with Roth's plan to "give a piece" to the Lakeville Road Boys, the Penino brothers, etc. If the deal had gone off as planned, Michael would have moved them out later. But for the present, he needed Roth's assent because Roth was tight with Cuban President Batista.
The great irony was that Michael and Roth were playing each other like violins: Roth playing Michael's lust to become "legitimate" by becoming Mr. Big in Havana as well as Nevada; Michael playing Roth's greed for the $2 million to buy time to find out who the traitor was in his family.
That's one of the reasons why GFII is such a great, great film.