It's not just that the UN that hasn't let Taiwan join, it's that the UN along with vast majorities of the countries recognize PRC as the legitimate government, and have embassies on mainland China. Even US does not have an embassy in Taiwan.

Meanwhile, I really don't see how you can draw parallels between Taiwan and Ukraine to be honest. I have to assume you don't know any history of Ukraine based on your statement. During USSR days Ukraine was part of the same country as Russia and people living in eastern Ukraine are largely ethnically Russian. That's why the civil war started after the coup in 2014.