here's the one thing you can't change.....that woman is HIS mother. right, wrong, good or bad, that's MOM. so there is going to be a weird loyalty there, that can defy common sense. remember, internally for him there is no CONTEST between his mom, you or the baby.....you each have roles in his life.
but what a freaking nightmare THAT was huh??? you totally have the right to say "not back in MY house!!" - and your husband has the right to say "i can invite my own mother to my own house if i want to!". which leads to a stale mate and somebody would have to make other arrangements.
since she seems underfunded, it's not likely she's going to be flying back any time soon, not on her own dime. so i think you have TIME on your side. you don't have to have the rules written on the stone tablets by 3pm TODAY. LOL
ACOA stuff is a sneaky, tangled beast. i'm 57, my A mother passed away when i was in my early 30s, stuff STILL comes up. good and bad. shows up in my dreams A LOT. my mom can be like reruns of Law & Order, no matter what channel you choose, there it is, again! i had this impulse to call her the other day.........sometimes i want to say i'm sorry i was so distant and cold those last few years. i am a mother myself now, and it's not that i try to NOT be my mother, i just try to parent DIFFERENTLY.
if you can, ease up on your husband just a bit. he didn't ask for this. and unlike alcoholism, there isn't anything you can STOP doing that makes you STOP being an ACOA. family of origin stuff is in our DNA.