You post touches me on so many levels and I might give some unexpected advice...
I speak from a personal experience here, since my younger sister had a child at 16. It is TOUGH for such a young girl and YES, she was neither mature enough nor did she have the resources to be a really good mother at that time. Her daughter would also spend considerable time with family members like yourself, but NO ONE ever thought that removing her daughter from her would be best for her or the child. My sister went through some tough times and at times even lost custody of her oldest children so she could battle mental health issues. And again, everyone was supportive, no one tried to take the kids from her. Through family support my sister made it. She put her life back together, overcame depression, was returned custody of her daughters and went on to a second marriage, having more children, taking in a step daughter and living a wonderful life in a blended family. She is the poster child for what can happen if a family REALLY comes together to support a teen mom.
I commend you for the help you have been trying to give, but it saddens me that your motives do not seem all that selfless at this point. I think you need to take a step back and examine your feelings, your actions and what you really believe is best for this child.
Frankly it does not sound like you are making much of an effort of supporting this girl's relationship with her mother. I don't want to bash you, it is understandable. You have taken care of her since she was pretty much a newborn and you LOVE her. That makes her a very blessed little person.
Maybe the mother does not want to be a mother and really, adoption would work out great.
But since you are worried about her reaction, I assume that she has indicated that she does not want to give up the baby.
As hard as it is, is there any way how you can improve the baby's relationship with her real mother? Can you ask that she picks her up every night (from what it sounds like she doesn't?). Can she spend time with her child at your home. Can you teach her how to interact with her daughter in a loving way? Can you show her how to bond with her child? Can you direct her to parenting classes or financially support her by paying for the registration fee for a program that promotes parenting skills and bonding?
You might be able to make so much more of an impact in these two girl's life, than just taking over and adopting the infant. And if you love this baby so much, would you not want her to have that bond with her mother?
Whatever you decide, I wish you and everyone involved good luck!
PS I would also caution you from going through CPS, if they do decide to place the girl in foster care, there is NO guarantee that she will go to you or other relatives.