It's the world (and not Soviets) who called it "the Ukraine". Ukraine was "the republic of Ukraine" and also considered as "the region" of Ukraine inside the "country" USSR.
Now that Ukraine is independent, it would be rude to add that article and keep considering it as "part of another country" or as a republic of the USSR.
More about this article issue: http://www.businessinsider.com/why-ukraine-isnt-the-ukraine-and-why-that-matters-now-2013-12?IR=T
The trema has nothing to do with stress, it's to indicate which vowels have to be pronounced.
Ai (without a trema) is used for instance in Thailand, it is pronounced like Scoub does here: http://forvo.com/word/thailand/#nl
Aï (with a trema) is used for instance in Oekraïne, it is pronounced like Scoub does here (maybe not super clear, but it has separate a and i sounds): http://forvo.com/word/oekraïne/#nl
Got it,thanks, I was confused because I knew about the eu, oe, ui diphthongs in Dutch, which sound different from their individual components, so I understood why you write ruïne, in the case of Thailand it sounds like draaien, and there the a and the i sounds are in the same syllable, unlike in Oekraïne.