Can Co-parent Who Moved Get More Custody Of Child?

I’m in New Mexico. I left my ex because of a DV situation and I have 80% primary custodial custody for about 7 years. At the beginning of 2024 the ex decided to move to another state and has only seen our kid every 6-8 weeks. They have had two our three overnights and the ex has taken her to see family out of state. It’s all been fine and low-drama. Now, because the kiddo expressed discomfort about being around the ex’s new partner (brought the new partner around for the holiday break), ex is threatening to take me back to court because I attempted to set boundaries at our kid’s request.

Because I am the custodial parent and have 80% custody and ex chose to move away, does ex have any standing in which to get MORE custody of our child? I have never blocked access to our child or prohibited contact or travel. I have set boundaries saying I will not send our child alone to another state, have told ex that they will need to come here to get our child, and have advocated for our child’s comfort and well being. It has only been since ex has gotten with a new partner that he has gotten combative with me. Does ex have any standing on taking me back to court?