Have you talked to your sister about her wishes? If I were the bride, I really wouldn't want to have my shower at Pizza Hut. Birthday parties, graduation parties, even co-ed showers maybe... Pizza Hut just doesn't seem very bridal shower-y to me.
However, if someone were giving me a shower, I would accept whatever, but, in this situation, since the bride is your sister, I would at least consult w/ her to get an idea of her preferences.
In our area, I've been to many, many bridal & baby showers hosted at different homes. I've also been to several that were in churches' fellowship halls, & I've been to some (not as many) that were hosted in area restaurants or tearooms. I've never been to a shower at a Pizza Hut though.
So, in answer to your question, while I don't think a shower at Pizza Hut is necessarily tacky, if I received an invitation for a Pizza Hut shower, I'd find it a bit unusual. I also really wouldn't like switching locations in the middle of the shower either.
Although technically the mother-of-the-bride is not supposed to host the shower, if your mother is willing to have dessert at her home, why not host the entire thing at her home - if you can't find another reasonable venue? On the invitation, though, just list yourself as the hostess & not your mother.
If you can't afford a full sit down luncheon (which was the reason your mother was suggesting Pizza Hut for the pizza & salad), host the shower in the middle of the afternoon. Turn it into an "afternoon tea" & serve tea sandwiches, little cookies, fruit, cupcakes, etc. That would go well w/ your thoughts for spring flowers too.
EDITED TO ADD: If your mother is set on Pizza Hut, maybe have lunch for the bridal party (bride & bridesmaids) at Pizza Hut, & then have a dessert shower later that same afternoon. The only ones that would be at lunch would be the bridal party, & everyone else would be invited to the shower as the "main event."