Mother in law and new baby is she overbearing?

I have a great husband and family. I always thought I had perfect in laws till now. They stayed out of our business and have been great with my son who isn't biologically my husband's. Me and my husband have been together for seven years and my son (who is nine now) calls him dad. This is my mil first grandbaby. It all started when I went into labor. I had said only my mom, mil and husband could be in the room. Then everyone else could come in after she was born. Well my mil brought her husband and her daughter. I was getting stressed because there were too many ppl in the room and my baby's heart rate kept dropping and when the in laws went to lunch my husband called and asked them to take their time (I wasnt even dilated to four cm) She started crying. When they got back we asked his mom to come in and she refused until I started to push. Right in front of my son after the baby was born she asked my husband how it felt to be a dad. (I haven't had "the talk" with my son all he knows is my husband is his dad) And let me also say that I know you can't help your feelings and I know she will be closer to this grandbaby than my son but all I've ever asked is dont show it. The baby was only three days old and she was asking to take her home with her for a couple of hours. We said no and I told my husband he needs to tell her that it'll be awhile before I let anyone watch her let alone take her anywhere. (she is breastfed by the way) She comes over at least three times a week since she was born, and stays two to four hours at a time. Also for the first three months my baby had colic. I was constantly having to walk around with her.Mil would come over and hold the baby when she was asleep, when my husband and I weren't looking she would change her diaper. She would say that she felt wet but I knew she was doing this to wake her up to play with her. Because she woke up my sleeping baby I would be stuck walking and bouncing her back to sleep.She always leaves as soon as she knows she cant hold the baby. Halloween I said I just wanted our little family to go out trick or treating when the baby was two weeks old. She showed up unannounced right as we started to walk out the door and then started crying because she could tell we were a little annoyed by it.(But we didnt say anything or act mean about it) She then kept asking if she could watch the baby while we took my son out. And when I said no she asked if she could come with us.(She never used to do this) Christmas before I had a chance to she went out and bought three baby's first christmas outfits. That would've been ok if she would have involved me somehow. She made a baby's 1st christmas keepsake and only put pics of her and the baby in it and only wrote about what she did with the baby and what she bought her for christmas.(It was a card she gave to the baby) Let me also say I was really young when I had my first child and didn't get to enjoy his first year because of my situation. I had to put signs up when the baby was a newborn to get her to wash her hands before she picked her up. The baby is teething now and she was letting the baby suck on her hands(my mother in laws hands) she didnt wash her hands before and she even said " Maybe I should've washed my hands first". Then on Valentine's day we told her we were gonna do our own thing and she showed up unannounced again and kissed my baby in her mouth!(GROSS)I cant let her do it and tell everyone else not to. Besides it's flu season!! She has been saying "Ive got a new picture frame that says grandma I need to find a picture of me and the baby" What about my son?? She has a Facebook page and its nothing but pictures of the baby and very few of my son. She has always called the baby "her baby" not "my grandbaby " but "my baby". She would pick up my son from school and he would ask her to come in and if the baby is asleep she wouldnt. My son said to me "nana doesnt want to visit me she just wants to see the baby and she only takes pictures of the baby" I just tell him its because the baby is new. She always brings gifts for baby and not my son. When she held her she would kiss her all over her face and talk to her loudly and (basically overwhelm the baby) she didnt like that so she would cry everytime mil would hold her. Mil would try for twenty minutes to calm her down while I go insane because the baby is screaming. I dont know if I should let her hold her while she is crying because I feel bad when I know she came to hold the baby and it was hard for me to take her from her, but its not fair to let the baby cry. My husband wont tell her not to do any of these things I've mentioned b/c he said how can I tell her not to love our baby so much. He sees her as this perfect person who does no wrong. I'm sick of arguing with my husband and dont want bad memories of my babys