From recent-ish personal experience...
We went with a 9yo with a broken leg for a 10 day trip. She had a cast on for about 5 months, and the cast was on during the trip in August. I don’t know what luck you will have getting a
DAS card - like you, I heard mixed feedback with some saying that you would be able to procure one and others saying it wouldn’t work out. We didn’t bother to try. Instead, the doctor authorized a wheelchair through our insurance company so it was of no cost to us. It was small and mostly comfortable. She could transfer using her crutches, but it wasn’t easy. Many rides we went to a designated space for loading people with mobility problems and waited for our turn to be loaded. I would say that we frequently waited less than the stated wait times and for some rides, they would send us to fast pass for a return time anyway.
As an aside, having her be in a wheelchair made people be a little kinder about our mobility issues and people gave us more space. When my kids were smaller, I sometimes found that people would make comments about older (4/5yo) children in strollers.
I was worried at first, but the vacation was great and I don’t think we missed out on much because of it. In fact, she often felt really special because cast members went out of their way to assist.
Good luck and have fun whatever you decide to do!