This is definitely a hard one.....Things have changed so much, and I don't think there is an easy way out of this. You actually have the legal right to severe ties with the mother and yet, these days, many adopted children eventually want to know their birth parents and are likely to rekindle relationships. Although I have not adopted a child, I do know that it is not much different from relationships that occur with extended or blended families. Without understanding all that is, personally, I don't think pushing her out of the picture benefits any of you. You can however set limits, and establish a relationship based on those limits. She is the biological mother but you and your husband are mommy and daddy. Your baby will eventually grow-up and the choice will be up to them, and this is the gray area. Do you stop communicating with her all together and not tell your child he or she was adopted, will you need (for medical or otherwise) the mother? In today's day and age, and for the sole purpose of raising your child well, you have to take into consideration all the other aspects.
Perhaps you can have her over a couple of times a year, have her establish a relationship for the sake of what's to come and the inevitability of you baby growing up. You are legally this child's parents and although I totally empathize with your feelings, how you may approach it may make all the difference in the world. Although some children may never want or need anything from their biological parents, statiscally, the majority do inquire about them, they want to know, that's just a fact. You cannot deny this for them, not if you love them. You can control the extent of your obligation though, you can control and limit the biological mother's expectations and demands to meet the need of you and your family's wellness. You are this child's parent now in all aspects and the two of you can move on with your lives, you had and have the power to do this at any time, even at this moment. You just have to realize that overall the obligation is not to her, it is to your baby, and with that in mind, discuss the details with your husband and set the ground rules from there.....DONE DEAL.....If I for whatever reason gave up my baby, my motherly instinct would far surpass any logical reaction so expect things to get harder before they get better, but they will get better when you realize this is not a dilema just another responsibility associated with being a parent! GOOD LUCK! May God Bless you and your newly found FAMILY!
Oh and one more thing....Your motherly instincts have kicked in.....you can tell by the tone of your request, biological or not, you're in! We're here and I hold up my hand to all my sisters in this universe who try to make the world a better place one little angel at a time! PEACE!