I agree with the suggestion that you try & make it work in Europe.
Been there, done that (twice!). Now stuck in U.S. Biggest mistake of my life...so far! The regional pay is absolutely terrible - my single mates can't afford to live on it & actually do have part time jobs in places like Publix/restaurants/bars etc to make ends meet.
You are in a very difficult situation. The question I wish I'd asked myself when in your shoes was "is my relationship with the mother of my children likely to survive the enormous upheaval of moving country/job/life/kids etc?"
It wasn't, don't see the kids now & am basically completely displaced from friends & family. If I do go home I could never afford what I had before & also lose any right of long term abode in the U.S hence can't spend much time with the kids as they grow up. My actions & subsequent decisions have effectively destroyed my life.