A disability can be temporary or permanent, it doesn't matter. If she needs the wheelchair to make her trip pleasurable she should get one.
Someone (I think it is Sue or Cheshire Figment) suggests finding a location that is about mile and ask the person to walk it and see how they feel, then do it about 4 more times because you can walk 4 or 5 miles in an average park day. If she can not do that comfortably then she needs a wheelchair or ECV.
It was me to start with, but a lot of other people have picked up on it - and that's great, if it helps convince someone they need to use a wheelchair or ECV.
Cheshire Figment has a great list of questions that basically boil down to if can answer "yes" to having problems with mobility and to wanting to have a good time without pain, you need one.
Also, if someone is worried about whether your wife is in a chair one day and walking another then that person needs to get a life. This is your vacation, you will not see these people again and she should do what makes the trip comfortable for her. Yes, in all honesty you might get looks, but in the end those people don't matter, what matters is her NOT in pain, having fun with her family.
There are people who will care, but like you said, those people need to get a life.
And, some of them will judge no matter what. I have had the experience of sitting on a bench in Epcot, next to my daughter, with her wheelchair sitting next to her. Some people stopped behind us and one said to the other, "There's one of those people who get a wheelchair just to get ahead in line."
He made the judgement based on seeing my daughter out of her wheelchair. He didn't bother to really look at her wheelchair to see that it was an obviously custom wheelchair with extra footstraps and a special seat.
All he saw was someone OUT of a wheelchair and decided that meant it was not needed. He also didn't see us lift her from the wheelchair to the bench since she can't stand by herself.
And, if he had followed us a while, he would have noticed that in most attractions we waited with everyone else in the same line.
So, follow the advice of the other posters here.
If you want information about renting, you can follow the link in my signature to the disABILITIES FAQs thread - post #2 has rental information.