We put her book in a clear plastic cookbook holder and set it on the table. Now she can fidget all she wants and the book stays still. She and I can both see the book at the same time a lot better now too! Just thought I'd share in case this could help someone. We do have to move the book from the holder to turn the page, but she is in chapter books now so it takes long enough to read the pages that it's not annoying. 
ETA: We have tried having her read while I hold the book, but this doesn't work, because 1. She's very independent. 2. She says she can't read it very well when I'm holding it.