Lazy Girl Designs makes an acrylic bag bottom. There are several sizes to choose from. The bottom is covered with a slip-on sleeve. I have made several purses and interchange the bottom from purse to purse. If you don't want to buy the bottoms. You could buy the acrylic plastic sheet and make your own.
To make the purse stronger on the sides. You can layer between your inner and outer fabric a product called Steam-A-Seam or maybe quilt the layers.
http://www.lazygirldesigns.com/produ..._E_Bottoms/c53