Dealing with MIL

My daughter is now 1 month old. It took 2 long years to concive her after 2 miscarriages. I also had a rocky pregnancy with her and we delivered at 37 weeks but she is perfectly healthy. This is my families first grandchild but my husband's 5th. My MIL is obsessed with my daughter she claims she is her favorite grandchild and constantly tells me how to raise her. I've had the talk with my husband and he has told her to back off now she is upset saying he is pushing her away and doesn't want her around the baby. When she was born cause of covid we couldn't have anyone at the hospital and she made it all about her and that I didn't want her at the hospital during labor. Everytime I tell her something about about baby she always says oh well my son did this so make sure you watch for it. 🙄 my husband was a huge mommas boy before he moved out away from her but she is so obsessed with him it's weird. She even ran to hug him and cut me off after the gender reveal which really made me mad.