Granny wants guardianship

So my whole fear having a kid when I was preggo the mom said she wanted custody.

Now I had the baby and the dad and I are getting some stuff taken care of (our relationship/ housing)

The moms a caretaker. She already adopted two crackhead babies now she wants my kid

Today my partner told his mom “don’t call me babe.” And she got MAD and went and did this haha.

How do I get out of it? I’m in the middle of housing atm and got calworks but can I fight this? Ima leave tonight to avoid signing but help