I went through the same thing when my daughter was less than two. She didn't like to wear the glasses either until her doctor tried patching the good eye in order to strengthen the bad eye. I had the exact problem when I was very little too and my eye was patched also. I believe that I kept my glasses on though. My daughter realized that she would rather keep her glasses on than have to wear the patch. You can purchase the patches at any drug store and cut them down a bit to fit the eye area better.
When I was working with disabled little ones at a special ed. school I had a few through the years that had to wear glasses, and you can imagine how often they threw their glasses during the day. Their specialists provided straps to wear around the back of the head to keep their glasses on finally after major repairs to their glasses. It worked very well and the kids finally realized that they had to keep the glasses on their faces. Good luck!