Single mom insight, here.
I assume your father is from another country? There are some countries where if a father brings a child, the mother has no rights. My neighbor growing up met a man from Africa, they married and had a little girl. When they divorced ( he was very abusive ) he threatened to take her out of the country. Remember the Dad with the son in Brazil? It took the death of the Mother and years to get him back. DD's father picked her up one day from school, and took her (only to the beach, I later found out ) earlier than his alotted time, and refused to answer my calls. The only thing I got was a text that said, "I'm not bringing her back" and I couldn't do a thing because it was his scheduled week. I cannot begin to explain how that felt.
You don't know exactly what went on between them, and the reason your Mother moved away. And honestly, he could have found you if he really wanted to. He wasn't involved, he didn't make any sacrifices for you, sit with you when you were sick, or make sure you had everything you needed, your Mom did. Now when you're self sufficient, he waltzes in and whisks you off to Europe, all expenses paid. Your Mom is feeling like everything bad he did ( whatever it was ) is totally negated by you going with him, and I'm sure her feelings are hurt and she's worried that she will lose you. And as a mother, I wouldn't want my child around someone who couldn't bother with them years ago. She's feeling very protective of you and the relationship you have.
You're 29. I think it's time you sat down with her, told her what you said above, and find out exactly what happened. It might help you understand why she's acting the way she is. And for what it's worth, I think the only thing she's trying to "hide" is something that happened between them.