Legal Question in Family Law in New Mexico

Whether there is trouble depends on whether the legal custodian complains.

Assuming there is a parenting plan in place, ideally, father would go to court that has jurisdiction and ask for a change of custody. Court is required to take into account (but is not bound by) the wishes of a child over 13. I would encourage little sister to follow that path.

If the bad living conditions amount to abuse or neglect then a report should be filed with Children Youth and Families Department which will investigate and can change custody, including looking for qualified relatives to take her. CYFD is a mixed bag, can be arbitrary and unreasonable, but they're sometimes the only option. If they are reasonable they have the power to do really good stuff.

If she runs away and gets caught by police or reported, she will fall into clutches of the CYFD anyway. That's not a good way for her to go, she may end up in foster care or a CYFD facility which I wouldn't wish on anyone. Again, I would encourage her to work with dad to get a custody change through the courts.