For this part–you’re screwed. She’s going to hate you if you are the only one putting limits on her behavior. If you don’t give the girl some boundaries, she’s going to hate you later, because–and this is trite but true–kids need boundaries. If you aren’t willing to treat her like she capable of controlling her behavior she’s going to think that you don’t care what she does–and that’s going to translate into you don’t care about her.
In any case, this is her father’s fault. No matter how her mother allows her to behave, your SO is the one allowing her to get away with things when she is under his care.
Run, run, run.