overbearing MIL obsessed with grandbabyi

my MIL is obsessed! DH and i went on vacation with her last week and every person we saw she told that "that's my grand baby in there" pointing at my bump. she told us as soon as she found out that she was going to stay with us for a month starting 2 days before my due date (she lives in FL, we live in OH) oh and the baby better not come before she does 😒 like i can control that.. at first we were like idk a month might be way too much. then we were like ok it could be a lot of help. but then this past week on vacation she not only told us that she plans on coming to our house one week a month every month to "relieve my mom of babysitting" but she also wants to be in the hospital room the minute after the baby is born. i'm defiantly not okay with that. DH and i need time to bond with our baby girl. i don't know what to do about this. when she told us all of this my sister in law was like no mom that's not happening they need time with their baby and MIL flipped out on her saying it's her grandbaby and she's going to be there the minute the baby is born and that she "needs" to be there and " grandmas trump parents". i didn't say anything just to avoid a fight with her (we were at dinner with extended family at a restaurant)  my MIL isn't afraid to make a scene to get what she wants and she's good at it. so much so that i'm afraid even if i do tell the nurses that we don't want visitors for a couple hours after that she will somehow force her way in the room. (she's an ER nurse and she'll probably use that as an excuse somehow smh)  any advice on how to deal?