I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about this situation.
No, the mother cannot take the baby away from the girl. The parents of a child by default have custody, even if they are minors themselves. The grandparents do not have any legal ability to take a child over the parent's objection - if she tried, it would be kidnapping. For the other grandmother to do anything, she'd have to file a Petition to have BOTH your son and his girlfriend declared unfit parents, which requires something more than just their ages. That requires a court proceeding, so if she tried that, you'd be able to intervene and show the judge why you should get custody instead (if the parents are found unfit - but they'll have a right to establish that they aren't). If for any reason Child Services is called to investigate by the other grandmother, you'll be able to talk to them.
The parents can also draft and sign something stating they want you to have custody in the event that something happens to them, but that typically refers to their untimely deaths while their child's a minor and not the type of situation you're talking about.
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