When other parent causes child to struggle...

Hi everyone, I hope this is the right spot for this, I need advice for my gf. Her and her ex have a non-court agreement of 50/50 share time with their child, I'll call the child R. The problems are my gf's ex doesn't support important decisions for R's growth and has a highly permissive and indulgent parenting style. R is 10 yrs old and should be able to do things on her own, but her father has her so spoiled that she can't do anything for herself and has zero desire to even try. When R is at her mom's house, she is encouraged to be independent, which R argues and fights the whole time. It is obvious R prefers being at her father's and has told us because he doesn't make her do anything. He is also causing further alienation issues by putting all the hard decision blame on my gf. He may agree with my gf about something R needs, but if it involves anything that makes R upset, like no tiktok or less ipad time, or enforcing consequences for misbehaving, he either wont do it or tells R it's because her mom said, not that they both agreed on it. Now it is obviously R is struggling with low self-esteem, school, and making friends. She doesn't listen to anyone, she thinks she can do what she wants without consequence and everything else is supposed to be done for her.

So more concern arises that R is going to be spending even more time with her father who is not supporting her personal growth or providing her with her own room/space, she shares his bed or sleeps on the couch, though there is room in his house for her to have her own room. Even in my gf's 1/1, R had her own room space with her own bed.

My gf has tried talking to her ex about handling R differently and supporting her more, but he doesn't seem to think anything is wrong. So I guess my question is, at some point can my gf file for full custody if R continues to struggle due to her father's influence?

Thank you!