I don’t understand “the NATO problem”. Even if Ukraine became part of NATO, all it would mean for Russia is that there will be consequences if they invade. How hard is it not to invade other countries, unprovoked?
Ukraine gave up its working russian-inherited nuclear warheads. So, no. This is not the same.
Putin is just another authoritarian ruler, a dictator. He will use any excuse he wants to invade; in this case he is using NATO membership and separatist movements.
In the practical sense, the "NATO problem" is that Ukraine is not going to give up on Crimea, and once it becomes a member of NATO that will lead to direct confrontation between Russia and NATO.