I’m not sure this will be any help, but we have a cat with similar problems (except we have a lot of children already, so she is adjusted just fine to children). She was abandoned by her mother at a very young age and the children brought her up with bread soaked in milk until she was big enough to eat.
We did get her neutered, and she chewed the stitches out. We returned her to the doctor and he stapled the wound shut. She chewed the staples out. He put a long wire-type thing in to hold it together and left the ends sticking out so that if she attempted to chew the wound, the wires would poke her. It finally healed. But she hasn’t been happy since. (That was over two years ago.) I am wondering if maybe she has adhesions from the neutering procedure and they hurt when she’s picked up or something. :-/
As long as she is treated like a queen and we remember which types of cat food she doesn’t like, she is okay. ;)
She does lose her hair in patches about once a year, mostly on her back in the rump area. Perhaps this is just a normal cat thing. It happens in late winter. It has always come back okay, so we have learned to ignore it.
If she feels that she is being “mistreated,” (i.e. we let another cat in the house, we give her the wrong food, etc.) she will mess in the girls’ closet (in the room she usually stays in when she’s indoors).
On rare occasions she becomes affectionate and jumps up on someone’s lap to be petted. But usually she just spends most of the day sleeping on one of the girls’ beds.
You may just need to keep her away from the baby. A warning: sometimes cats that feel that they have been replaced, or who can’t deal with the stress of a new situation, run off and don’t come back.