Baby Shower Invitation Drama

Anna
I moved across the country four years ago to attend graduate school where I met my husband. For clarification, he is not a graduate student. We are expecting our first this February and his mother has graciously offered to throw us a baby shower. I don't know many people here outside of his family or my program and all of my friends here are from my program. 
When I moved here I became very close with Katie and her boyfriend Connor. Connor and I have drifted apart as he wasn't the nicest to my husband when he and I entered our relationship, but Katie and I are still close. As you can imagine though, the minor falling out with Connor has put a slight damper on Katie and I's relationship. Also, when I initially started the program I was their neighbor and we would hangout nearly every night and since I moved in with my husband we only see each other if I make the plans. In my absence another graduate student and his wife, Zoe, have replaced my nightly hangout sessions with Katie and Connor. 
I really cannot stand Zoe, she became very possessive of Katie very quickly to the point where myself and the rest of the girls in our group of friends have been seeing less and less of Katie. This is partly because Zoe is always around and partly because Katie never makes plans, you always have to contact her. While everyone outside of the Katie-Connor-Zoe-Adam foursome doesn't like Zoe, she is always invited to events because she is friends with Katie and so she is apart of the group. I should also mention that I was guilted into inviting her to my bridal shower and wedding where she stole people's attention every chance she got. She has also made a point to leave me out of gatherings that she has arranged. To put it short she is a friend of my friend and considers herself in our group, but I find her to be an attention seeking manipulative bitch. (Ex: when I was shopping for my wedding gown and people complimented my ring she had to tell us a 30 minute story about her sister in laws ring is 3x bigger, and instead of helping me find a dress she was having Katie help her find dresses for herself... when she was already married.)
Should I invite her to my baby shower? She has already made comments assuming she will be invited and if I don't I know it will put Katie in a weird position and I have done everything to avoid putting her in the middle. I also think some of Katie and I's mutual friends will think it's petty somehow and that I should just invite her to keep the peace, but I just don't want to. I feel she always gets what she wants and I end up suffering as a result. 
Advice please!