It's not rude, per se, but that doesn't mean that her feelings (or your FI's feelings) won't be hurt. I know my FMIL would have been VERY upset if I hadn't asked her to go with me. Try to explain to her that you want it to be a surprise, hopefully she will understand.
It could be a nice gesture...especially if she doesn't have any daughters. It could also be a chance for her to get to know your mom a little bit better.
Re: dress shopping