If she does not want to sign over her rights, it could take years for you to get full legal custody. You would have to go to the department of social services and file a claim that she is being an unfit parent. They would investigate this and see if she really was. They’d probably give her a warning the first couple of times you file, but eventually, if you’re persistant, they’ll take away the child and put him in foster care. Once in foster care, they’ll give her a chance to straighten up. If she doesn’t, they’ll take away custody, and that’s when you can step in and offer to adopt the child. This whole process could take YEARS to go through if she refuses to give up her custody.

You’re better off sitting down with her and asking for guardianship. That way, she still has partial custody, but you and your wife also have parental rights. It’s kind of like you are all parents to the baby. You have a say in all that happens to him. She can’t take him away without your permission, she can’t do anything to him without your permission. That way, should she refuse to straighten up, it would be easier for you to go to the courts and petition to get full custody, instead of your guardianship status. This way will take a while too, but not nearly as long.

IF she will cooperate and hand over custody, she can file with the courts to hand over her rights to you and in a matter of months, with a small fee of 50-100 dollars, the child is yours.

As for if they actually will take custody away, it’s hard to say. If she’s not actively doing drugs, chances are, they will not take him away. Courts actually like for the mothers to be with their children. It really is best for the child. Even if she’s doing drugs, unless they see it as an immediate threat to the child and she’s been caught by the law, or something for proof that she’s CURRENTLY doing them, he won’t get taken away.

she has been to rehab and if she stays clean adn shows she is able to take care of her baby then i am sure they will give her a chance

In one way its kind of sad that a baby born with drugs in their system isn’t taken away. But helpful here. The Dr knows the situation. The hospital will also know so the baby can get proper care if needed. They will both be tested, if your daughter has managed to stay clean (and I hope she has) its evidence that she hasn’t used in a while. and helps towards showing that life is behind her.
It’s not cause enough for cps to take the baby. They will most likely be involved with all of you for the first year or so to make sure that she’s not into that lifestyle anymore, and that your grandchild id being properly taken care of.
CPS also prefers that children stay with the family. If they deemed it necessary for her to not have the day to day responsibilities on her, you will get first “dibs” for lack of better wording to the custody of the baby. She will have a set list of things to do before custody is given back to her.
With you and your wife with her, you should be fine.
Maybe see if you can get a free consult with a family lawyer in your area, just to make sure what the options are here. I’m almost positive you her and baby will be fine, but laws like this vary wildly from state to state, what I’ve mentioned is how it is in Alberta.