You'll have enough people to talk to at your wedding. Just invite her. Not doing so would send a message so aggressive, it would likely create ongoing problems in the family and isolate you and your husband. It's hard for me to tell if she is being intentionally rude or if she's shy or something else entirely. But you do point out that she'll respond to you when asked a question, so it doesn't sound like she's being intentionally cruel.
It should have been a red flag when she walked up to the altar beside her son and said, 'You don't have to do this.' Eventually, he told her to sit, and we finished the wedding. She went through my drawers and complained to him about my pricey underwear, only to find out they had been a gift from him.