My husband and I are looking to adopt my 6 year old niece who is currently living with my mother. Her birth mother signed away her parental rights a few months back. My mother is fine with the adoption because she knows we can provide her with a good stable home. My question is what would the first step in the adoption process be for us and even though she signed away her rights could her mother try to stop it if she decided to?
The first step you need to take in this case is to find out who has legal custody of your niece. If the state terminated the birthmother's rights they may have placed your niece in foster care with your mother, or they may have made an adoptive placement.
If your niece is in foster care (which means the state has legal custody but your mother is the foster caregiver) I would suggest that you and your mother talk to the social worker overseeing the case and explain that you would like to adopt your niece. They can then tell you if this is a possibility and what the next steps are.
If your niece has been adopted by your mother (by which I mean a finalized adoption) it would not be possible to adopt your niece. If the adoptive placement has not been finalized you should still talk to the social worker overseeing the case about possibly adopting your niece if your mother is not interested in finalizing the adoption.
As for the mother of the birthmother stopping the adoption. It is possible that she could step forward and say she wanted to adopt your niece. The state prefers to place with family, but will only do so if it is in the best interest of the child. In a situation like this where two family members came forward they would probably evaluate both families and determine if either is a good placement for the child.