Do I invite FI's female friend to my shower?

Yes, be the bigger person - ALWAYS - never want the other to make negative assumptions.

I think the better question to ask is why doesn't she like you and why isn't she going to the wedding even though it seems like she can afford it? I would never skip out on my best friends wedding. I hate to say it, but it kinda sounds like she is jealous and harbors feelings for your FI. Especially the fact that you feel this weird vibe that she doesn't like you. Listen to your gut instinct.

That said, I may be wrong. I say just invite her since it's never to late to try to be friends with her. That way, you can't say you didn't try.

I agree w/the ladies. You need to invite her. If she comes good. If not no skin off your back.

Ive been there with the "friend since hs" crap and we just don't like each other at all. She wasn't invited to anything of mine wedding related as well as our wedding.

I would invite her. She probably won't show up, but at least you are doing your part to keep the peace.