This situation, though painful, is not uncommon when parents divorce. Parenting is always challenging. (It’s just true that babies don’t come with instruction manuals.) It’s made all the more challenging when parents don’t live together and especially if and when the couple hasn’t figured out how to co-parent while living apart.
Here’s my first pass at a different understanding of your situation (granting that I have limited information). I don’t think you are wrong about your observations. I do think you may be mistaken in your interpretations. I’m not at all sure that the girl is “manipulative” or jealous. From my point of view, the kid is scared. She already “lost” her dad’s time and attention due to the separation from her mother. She may unconsciously fear that he will leave her again. She may believe that there isn’t room in her dad’s life for the two of you so, of course, she is trying to push you out.
Her dad is inadvertently supporting her anxiety by giving in to her. My guess is that he is feeling guilty for the divorce or due to the fact that he isn’t a full time dad to her. He is compensating by giving in to her demands and making her the center of his universe when she’s around. In his attempts to reassure her, he is creating and maintaining the behavioral problems. But he doesn’t know what else to do to show her he loves her and won’t abandon her.
An unhealthy cycle has gotten going: The girl is scared and insecure about his love. He feels guilty. She feels she can’t get enough of him so demands first place in his attention. He overcompensates by giving in. She gets reinforced for the demands. He feels like, at the very least, he can please her when she’s with him. And so it goes. You don’t have a place in the cycle. If you try to intrude, they both push you out.
You are right that this isn’t healthy for anyone and it isn’t good for your relationship. But you won’t get anywhere by trying to “correct” your boyfriend’s behavior. What needs “correcting” is his guilt and his mistaken idea about how best to love his daughter. You probably can’t do that.
I hope your boyfriend will be open to the two of you seeing a family counselor for a few sessions to work on this. It’s important that the situation be corrected now – before the teen years when things are likely to become even more complicated.
Your boyfriend needs some practical help and support while he shifts his behavior with his daughter. You need to learn how not to take the situation so personally and how to be appropriately supportive of both father and girl. The daughter does need to understand that her role with her father is different than yours. I am also concerned that she be helped to understand that love from a man isn’t measured by how much he gives in to her demands.
Do inquire about the counselor’s training and experience. Although some certainly do, not all psychologists and counselors have the training and expertise to deal with the complicated family dynamics of divorce and adolescents. I suggest you look for a licensed marriage and family therapist (LMFT).
I wish you well.