She’s just being a very excited aunt, i know I was when my nephews were born and before I had my own baby I felt like they were an extension of me. Still love them like crazy 🤍. I say it’s a good sign that she’s so loving and no matter how quirky in-laws can be, encouraging a close and good relationship is a good thing. It could be sensitivity, not sure how far out in your postpartum journey you are. I know I was very sensitive to anything my in laws did the first 8 months I’d say… If you want more privacy and control around how they access your family, living on your own with your husband would be the best option.
I dont think she is being like a mother to him, she is being a very excited auntie who loves him. Is this the first nephew/grandchild on that side? My nephew was the first one and we all gave him so much attention etc Its out of love and not because she sees herself as his mother. Are you close with SIL etc? Because I find it jarring my partners family being like that with my daughter. I think because I didn’t have much of a relationship with his family.. when she was little it was too much! Even though don’t think they meant harm