How do I (30f) get friend’s wife (28-29f) to stay away from my kid’s birthday party?

Hi there! Looking for some advice!
First some background:
My husband and I moved to a big city a few years back and reconnected with an old friend E and his now wife J. I’ve known E since we were in high school and we were pretty close friends. Since we’ve been seeing more of each other I’ve gotten the chance to get to know his wife J. She’s nice enough but she’s the queen of over sharing to the point of making my husband and I uncomfortable. She goes into detail about her sexual relationship and it’s just really inappropriate and gross. I know things about her and her husband that I really wish I didn’t. She’ll even talk about her brother’s sexual preferences and his likes and dislikes which seems SO ****ING WEIRD.
She’ll come over to my house (because she knows I’m a SAHM) and overstay her welcome. She’ll stay until like 8-9 or even past that on weekdays when my husband has to wake up at 3am for work. She’ll raid my fridge and pantry and lay on my couch all day, rub her feet on my throw pillows and couch. She’ll be really loud and obnoxious so my baby can’t nap because she’s taken up residence on my couch for the day. It bothers me a lot but I’m too uncomfortable and frankly scared of raising objections because she will blow up and make a huge fight about it and I’ll basically lose my friend E over it (she’s done it to other people in our group of friends).
Anyway on to the issue!
My baby is turning 1 soon and we’re planning on having a small intimate birthday party with family only. E and J have a wedding to go to that weekend that J doesn’t want to go to because she hates the bride (who is E’s best friend). She said she was going because it would mean a lot to her husband. Well, I found out through a mutual friend that J is planning on skipping the wedding and staying in town for the birthday party. I really don’t want her there because she requires too much attention and I would be having to cater to her instead of my family. I would be so anxious about her being there saying all kinds of inappropriate **** to try and get attention/laughs around my in laws and family.
She doesn’t know that I know she’s coming and the birthday party is in two weeks. How do I make it clear that she’s not invited without it blowing up and losing my friendship with E?
TL;DR Friend’s obnoxious and entitled wife is planning on coming to my baby’s birthday party and I don’t want her there because she is awful and rude. How do I get her to stay away without damaging my friendship with her husband?


Source.