Unenthusiastic bridesmaid

Hi everyone! I’m in a bit of a pickle and could use some advice. I’m getting married in October and I’ve asked 9 beautiful girls to be by my side- all who were very excited and said yes. The planning has been going smoothly and (in my BM’s words) I’ve been a super easy going bride. There has been zero drama- I genuinely want everyone to be happy, not just me. One of my girls is a very close family friend who I introduce as my cousin (we all have those, right?). There is an age gap between her and the rest of my girls, but my sister-in-law who is a BM is around her age, too. Throughout all the planning, my BM’s have asked me if my cousin is okay as she doesn’t respond to any messages and no one has talked to her, including my MOH. When it came time to getting our dresses, I was very open to seeing what everyone was feeling, but my cousin was the only one who couldn’t make it. Everyone else agreed on a dress and we were in and out of the shop in 45 minutes! All the girls had ordered their dresses a few months later, but my cousin kept putting off ordering hers. She said she was working and the hours the shop is open doesn’t work with her schedule which I knew wasn’t true. Mind you, my friend who lives in a California (we’re in NJ) was able to order the dress and get her measurements in with no problem. I told my cousin if it’s easier for her, she can get measured anywhere and just call the shop. After months of asking her if she’s had time, I had to lie and tell her the owner of the bridal shop says she NEEDS my cousins measurements ASAP. She finally did it. She also showed up sloppy, very late, and less than happy looking the day of my shower. I know she has a lot going on personally, but I can’t help feeling like she’s not excited to be one of my BM’s and I feel selfish for saying so, but I don’t want anyone by my side who isn’t truly happy to be there. I want her in my wedding, but only if she’s going be happy doing so. How can I gently ask her if this is absolutely something she wants to do, without sounding like I’m trying to give her the boot?