Immigration isn't driving unemployment in the EU. Foreigners aren't taking natives jobs. They're given the same wage as a native, given that they often don't speak the language of the host nation they are in the native will always be hired first in a head to head job application. They're taking jobs that are either simply available because there's a demand for workers or they're taking jobs natives don't want.
Immigrants in the UK are far less likely to be unemployed, take far less benefits and pay more in taxes than the average Brit. The employment problems in the UK, at least, are domestic problems they have little to do with immigration. Immigration is a scape goat.
I'm not sure the Ukraine will join the EU immediately. This whole debacle was by the president reversing his decision to force closer ties with the EU, it wasn't like they were going to be accepted immediately. If they are it will be from a foreign relations stand point as opposed to an economic one as I'm pretty sure the Ukraine doesn't meet the economic criteria for EU membership.