Kate, my opinion would be to follow your heart - I can hear how very important this is to you, and I think that you just need to listen to your gut, your heart and your intuition and go with that - and be okay with going alone! Wanting to meet your relatives within the context of finding out more about your Dad is perfectly understandable. Again, IMHO, your Mom should try to understand that need in you and give you her blessing to go.

Is it possible that she doesn't really want to go, but might be playing yet another control/guilt game with you?

What if you compromised with her by asserting your intention to go to Denmark alone this time, but make plans to take another trip just with her, somewhere she'd like to go, like maybe one of those shopping trips?
_________________________
When you don't like a thing, change it.
If you can't change it, change the way you think about it.

(Maya Angelou)