Let us first break your problem into its components:
- A child who has never known what it is to share a parent with another "parent" and thus sees your boyfriend as a competitor for your love (Related article: Divorce can destroy families)
- A boyfriend who is simply rattled by this situation and does not yet fully appreciate what it takes to raise a child particularly when it is grown up enough to fight for her "rights" (whatever she deems them to be)
- In the midst of this, you need to be there for your daughter as you have always been, but at the same time rescue your relationship
How to make a child appreciate the presence of another 'parent'?
Your daughter's behavior is not unusual since she has always believed that she was the only one who had a right to be with you. This behavior is very common among children raised in single parent households in which the parent gives more than s/he would if the other parent were around. Such children not only do not appreciate marital relationships they themselves have more problems in their relationships when they grow up. There are a couple of things that you and your boyfriend need to do:
- He has to assume the role of a 'parent' even if he has to just learn it sooner than he would have liked to. He has to be the one to break the wall between him and your daughter so that they can establish an amiable relationship
- You need to educate your daughter about the importance of the relationship for both you and her. Indirectly, you should expose her to other families with two parents and how you should also be like them some day and how she should be like other kids
- Send her to a therapist
- Enroll her in activities that she she should do on her own (e.g. sports or arts or other activities that people in her age group do)
- While it sounds less romantic, but you will need to bring her along on some "dates" turning them into "family fun" rather than quiet, romantic time with your loved one. Hopefully, you will not need to do this forever
How to make your boyfriend appreciate the challenges?
It is evident that he has done a great job so far in being patient with you and your daughter. He also does not seem to mind that you are older and have a child. I will not expect him to run away at this stage. You are doing the right things by communicating with him and asking for his patience. If he can try to become your daughter's friend, she will learn to accept him and that is what he needs to do. Right now she sees him as a competitor rather than someone who will give her as much love as you do, or in other words, she needs to understand that she could get double the love by being friends with him. So let him have some private time with her, e.g., let him take her to the mall some day without you being present.
How can you balance everything?
First, don't lose hope. This happens to a lot of single parents. Many parents like you, because they feel guilty and want to give everything they can to their child, often end up giving a bit more than needed and also do not teach them what a normal family would learn on its own ("sharing"). You might need to be slightly firm with your daughter as well and not tolerate unreasonable behavior. She needs to know that you are a human being too and not just a slave to her wishes.
Dating after divorce