Heirloom makeup table

I am fairly new to woodworking and my wife was given a faimly heirloom makeup table. From what we know about the table and the style we think it was made 1920-1930s. There outer and inner walls on the legs are plywood and they are rotten. I am looking to replace them, the plywood is slipped into the furniture and then the base acts as a stop. The joint is just a groove down the center of the wood and is square and the bottom is glued in place to hold the plywood in place. I am trying to figure out the best way to unstick the glue. I would have to guess this is hide glue???? I am not sure, but would appreciate any help, thoughts or tips.