How to handle an overbearing mom

My boyfriend and I are expecting a baby together and I have 2 kids from a previous marriage. Hes perfect and were great for one another, but have our issues just as anyone else. let me tell you tho....HIS MOTHER. Lord I cannot stand her and I'm losing my patience with this woman! Me and dude have only been together 10 months and I'm 8 months pregnant so when I first meet his mom after 3 months of us being together he thought we should tell her I'm pregnant. I disagreed saying it might rub her the wrong way but we did it anyway and she made it known she was worried with how quick our relationship was moving but was excited he was getting the family he wanted. She comes off at the beginning as super sweet, wanting to include my kids in her family too says her grandkids call her mimi and mine are now her grandkids too. Takes me out to lunch that following weekend to ask the usual what happened with the kids dads and expressed her worried to me as I expected, well fast forward to last Christmas when we decided to tell the rest of his family were expecting, she follows me into the den where it's just her and I and says to me she just doesnt know how I'm gonna do it with my kids being so close in age and we should wait another 4 years before having another one....uhmm ok? Over stepping a bit. I didn't say anything but itll be fine and good idea then walked out. As time went on she would invite herself over and not only that but stay the night without even asking. One time she stayed for 3 days in a row and kept accusing me being upset with her to my man causing a bit of drama between us. He then had to force her to leave bc it was too much drama for all of us with her there and she cried about it. We then move into our new home a week ago and she starts doing it again. She told us she was coming by to pick up my kids so we could get things moved in and settled and she'll have them from Friday to Sunday. 🙄 please. She got here at 7 PM Friday and as I was frantically getting the kids ready to go with her she looks at me and dude and says oh I just planned on staying the night tonight since it's so late. I asked him later when it was just me and him did she ask him if she could just stay? He said no she didn't so we both got kind of annoyed. Then she ends up staying up till 12 am doing dishes? Wtf right? So I go in there and say thanks for kinda helping me with my list (my things to get done in the new house lidt) and she says all smartassy "kinda? And how did I just kinda help!?" I said well cause I have other things on the list to do still....took me back that she got upset about it like that but I just walked off. She leaves at 1 PM the next day with the kids and returns Sunday around 3. My mans wasnt feeling good so he went to lay down and when hes out of sight he mom goes outside, starts looking around the house then disappears for like 30 minutes. She comes back in and ends up barely talking to me but snooping around the house UNTIL 8 O EFFING CLOCK. Then when she finally says something to me, she hands me 400 dollars. Says "this is a housewarming gift, I'm giving it to you guys because I know if I ever needed anything from steve (my dude) he would tell you hold on my mom needs me. .." I laughed at her man. She is starting to really say dumb shit now when he isn't around and I cant believe it. So my thing is, what the hell do i do? Hes talked to her since then told her she cant stay over anymore because we have too much going on, she still asks to though, and quite frankly i don't think he sees this as much as a big deal as I do. She also is very adament I breastfeed which I cant produce milk so I've been told I'm supposed to tell her we are anyway just to avoid her getting upset? I feel his mother is too invasive and we are really starting to have issues bc of it. I just dont know how to handle her or what I can even do to get her to stop saying weird stuff to me when hes not around and stop dropping in whenever she feels like it. I told him I feel like this relationship is starting to be a trio and I'm putting my foot down. Hes already talked to her but shes already coming down again this weekend! Please gimme advice