Then what's a better alternative to resolving the question "should Ukraine join Russia?" if not by some kind of democratic solution (either direct democracy or an elected representative deciding)?

Ahem, that's the caricature simplified version of democracy you see used a lot by Western capitalist think tanks meant to discourage people from democracy.

Protections of minorities are by most republics understood to be integral to a healthy democracy. Not simple rule by majority. That's why most voting systems are not FPTP.