There are a few things you can do ahead of time to see if she needs a
scooter or not. On a local level the best one is to a day at a zoo walking around and see how it goes. Most zoos have a scooter; so, if she gets tired there you can rent a scooter right then and there and she can get some practice in on scootering at the zoo. Another version of this is to go to a museum for a day. If you have a pedometer use one and see how much she can walk in a day at these places. Another factor is you will be walking many days in a row, not just one day; that takes a toll.
Below average walking in a Disney park is around 6 miles a day. I would say the average is like 8 miles a day. The diehard fan can go beyond 10 miles a day.
If she won't scooter you can alternate activities so she can have rest periods. For example, do a ride and then a show attraction where you can sit, do another ride and have a snack sitting on a bench, then do another ride and see an exhibit, and then do another ride and break for lunch. I would possibly avoid long waiting ride queues like with Toy Story Mania in Hollywood Studios. Soarin' in Epcot has a very long trek before you get to the actual ride and that might be a bit much. Some rides like Universe of Energy and the Great Movie ride provide a good rest while you enjoy the ride. You need to get a little smart on planning the day; so, she can survive the walking.
My husband uses a scooter and it's worth every penny. The cost is well worth it because you last so much longer at the parks; so, you get better value on your park ticket; so, it offsets the cost of the scooter. Also, he is much happier and less tired on a scooter and he lasts for a longer day that way.
The decision to rent offsite or on site depends on a few factors. If you are early to the parks chances are very good you will secure a park scooter. You won't have to worry about getting the scooter on and off Disney transportation or in and out of your car, and you won't have it in your resort room and you won't have to charge it every day. You get an advantage if something goes wrong with a Disney scooter you can get a replacement very easily at the park and a CM will help you at the Disney park. If you use an outside vendor scooter you have it to use every minute of the day. This can be helpful; because, you can do a lot more walking out of the park. You can get a smaller scooter which will be easier to use. You will have to charge it every night and get it into your room each time. If you do have trouble with the scooter you will have to contact the outside vendor and wait and wait for someone to come to help. If you are in a park many of the outside vendors if not all expect you to get the scooter to the entrance for service.
If the scooter is too hard to handle in certain situations like on and off Disney transportation then someone else could do it for her. As others have stated you can park the scooter and walk some at the parks. You are not married to the scooter.
If this is a monetary decision then maybe you could treat her for a rental scooter and give it as a birthday present or whatever.
I just tore cartilage in my knee and I'll be using a scooter when we go to Dollywood in a few weeks and that is a much smaller park. Being in pain is not my idea of a nice vacation; so, I will use a scooter.