Thank you for writing. You are asking very important questions. It doesn’t help to call yourself names like “jealous” or “immature”. This is a difficult situation. It is very much to your credit that you are looking for some advice instead of just getting angry.
You are correct that your boyfriend will always have a connection to his ex because of their child. That connection has nothing to do with love for her, but it does have to do with love for his child. I do hope that he will see a lawyer regarding his rights to visitation or joint custody.
This child is part of his life and will, therefore, be part of yours, whether or not she spends time with you. Your boyfriend and his family are grieving the loss of the relationship. It speaks well of them all that they continue to hold that child in their hearts. That doesn’t mean that they won’t also love and cherish your child.
My best suggestion for you is that you support your boyfriend in his efforts to include his child in your family life. Instead of seeing the little girl as a threat, consider that she is part of the man you love. It is not the child’s fault that her mother is posting negative statements. It is not the child’s fault that she can’t see her daddy. She is just a little girl who needs her father’s love. Hopefully, you will get the chance to love her, too.
Encourage your sensitive, kind-hearted man to talk about his feelings. Let him know that you support him in getting time with his daughter and including her in your family. Love is one of those things that only grows the more it is shared.
I wish you well.