I went to WDW during my prep for my second round of treatment (hair was up to about 1/2-1 inch back out), and I still sported my wig some of the time. It was so hot that I had to seek out hats to cover my face and healing neck tissue. They had a lot of hats at the hat store on Main Street in MK and also in Downtown Disney. I still have one hat that was kind of a big floppy straw and then a soft cotton hat (think fisherman floppy, downward pointing brim that is uniform in length all the way around). It was white and lovely. It could be washed as well, which was super-important to me. The radiation treatments left me hot and cold and everything had to be washed a lot.
My thoughts and best wishes extend to your mom and your family! It's rough, but she'll fight through it! The hat will make her day!
Oh! And if you go in winter, they have the cutest Santa hats with Mickey ears on them. (You can also check in the Disney outlet in the outlet store in Orlando, if you run out of time near/in the parks)