How to act around the mother of your boyfriends baby?

My boyfriends daughter is about 8 months old. her mom and my bf were never in a relationship and when she got pregnant she wasn't sure if the baby was his. When he found out that she was his daughter we had started talking about 2 months earlier. Our relationship has progressed steadily and we are in love. The babys mom wants a relationship with my boyfriend for the sake of their child but he doesnt want one. This is such new territory for me and im not sure when i can say something or when i cant.. They are doing shared parenting and he is with her when he is not with me so that he can be with his daughter. I have no idea how to act in the situation, its awkward and uncomfortable i love his daughter but what if i dont like her mom and she doenst like me..?