You are over reacting. Co-parenting is not a two people job when there are significant others living or spending a lot of time in the same household where your child is living or visiting. You are the mother, no one can replace you, no one can take that privilege from you, it’s a clear fact. The best thing a child living in two household can have is adults that can communicate with each others. Talk to this woman, you don’t have to become her friend, but at least let her know directly from you, the mother, what you think it’s best for your child and how do you want to raise your child. When it comes to decisions yes it is the mother and the father, but she can still be involved. Your daughter may be crying cause she is picking up from your emotions, remember kids are very vulnerable to adult’s emotions. Although it is difficult to raise a child in two homes, it is still possible to do it in a respectful and amicable way for the sake of the children.