Op, it sounds like you have given your dd the most lovely life, and she is a bright child with lots of options and opportunities for her future.
I recognise the pain in your post, the frustration of raising a young soon to be teenager alone, and the clash of personalities you describe sounds particularly taxing. At least in part because her father gets to be Disney Dad once a year, and you are here doing the actual parenting every single day! It’s very unfair.
It would be fair to increase her visits possibly. Potentially offering you more breaks, and space to focus on your job/life.
Do you have good friends? And a close community where you live? Hobbies? I know you said you didn’t have an extended family.
Maybe it’s time for you to look into broadening your own life now she is older op, so whatever dd decides to do in the future you will be fine. Planning for an empty nest is something we all have to do. There are no guarantees that any adult child will remain close to home.
Some of the posts on here are really helpful, and they share your experience of parenting across two countries. Can you get in touch with other parents in similar positions? I would imagine that support and experience could be very useful.
Many of my own Spanish friends moved here to work, and have never returned, they would love to work closer to their families. Future employment, prospects and security will be utmost in your mind, but also general well being and living standards.
At the moment you are in the driving seat, if she lives in Spain are you ready to hand over the reins fully? It seems that after six months you would lose many of your legal rights - so it is a risk. I think getting solid legal advice is a good idea.
If you and dd were especially close as she grew up, this might be the natural development of independence which can be fraught. She may say things she doesn’t mean, but being there for her navigating the teen stage would be my first priority. My teen dds needed me more than ever from
rhe ages of 14-20yrs it can be a bumpy ride with hormones, new experiences, SM, first love etc.
Best of luck op 💐