Is it permissible to travel to a European country for a high-paying job with the intention of settling debts, while preserving one's religion, or is it better to remain in Yemen with a moderate salary?

We advise you to perform Istikhara (prayer for guidance) and travel to Yemen, asking Allah for blessings in what you earn there. Traveling to disbelieving lands is a concern for the one who undertakes it, due to the fear of being tempted by the manifestations of corruption found there. As for Yemen, mosques and people of knowledge and goodness are abundant, and it may be easier for you to perform Hajj and Umrah from there. If you can take your children with you, you might find an environment there that helps them learn and preserve their religion.