To invite or not to invite?

So my father-in-law recently remarried and my mother-in-law is now saying she’s uncomfortable around his new wife. (Mind you, she herself remarried 5 years ago and no one complains about him) I don’t want to be rude to the new wife and not invite her to my shower, but I also don’t want to upset my mother-in-law. I’m not really close with the new wife, we have actually never said more than a few words to each other. I try, but she’s very stand-off-ish. But I just don’t know what to do. I don’t have an issue with her, it’s my mother-in-law who does. So what would you do?