Should I trust this girl around my SO and baby...? (Might be a little long)

There's this girl who I recently reconnected with after her breakup with my SO's friend. She attended my baby shower and was always supportive from the start when I first announced that my SO and I were expecting. She actually knew my SO before I did. They were pretty close a few years ago but fell off because they didn't really have no business with each other years later. Well during my baby shower, she ended up getting REALLY drunk and messy and just kept going on and on about how her and my SO were close and they'd always hug each other when they saw each other. It didn't bother me because I knew they were friends and at the time I was cool with her too because we would have little double dates when she dated my SO's friend. There would be little things she did or said at my baby shower that kind of annoyed me, especially the fact that she was really drunk. She pretty much pulled out her titties to show how big they were when all of the guys were right in front of us. There was also a point at my baby shower where I went inside my house to start cleaning up and during the time I was inside, she felt the need to go to my SO and ask if they were "cool" and asked for a hug. Immediately after that, my SO walked inside and said "um...just to let you know. But so and so just hugged me. She just asked for a hug and I was like sure..." of course I was irritated but brushed it off because it was my baby shower and didn't want to have unnecessary problems. Then I again I thought to myself, "why didn't she hug him while I was outside? Why did she wait until I left and went into the house?" She said that she wants to be close with me and wants to be a part of my baby's life, and how she wants to have sleepovers and movie nights... and in my head I'm just like "I'm about to be a mom. I live with my SO. What are you thinking?" This girl also always brags about being a hoe and getting dick all the time, and how she wants to ruin relationships for fun... I really don't want anything to do with her at this point but she's so pushy about being in my life. Any advice?! 🙄😓