(they don't need to invade it, just to support a puppet president, that will keep supporting them afterward)
This is difficult without hostility, especially after Ukraine has so well established what direction they want to go, if we talk about democracy. The people
and the armed forces want to move away from Russia. If Ukraine then had an election, where it just seemed like all of Ukraine wanted Russia back in the fold, the population would obviously get wise to the scam at work, and rebel against it.
In that sense, it is easyer for Russia, if they are that dedicated, to move troops in beforehand. To expect hostility.
Same as they cannot invade _only_ Crimea, imagine the waste of resource to fight, fight and fight inside Crimea, while the Crimean defense (Ukrainians) have the rest of the country to retreat into and regroup. Even with little Georgia, you could see how Russia would move way beyond their "claims", precisely to disrupt the Georgian military efficiency.