They are usually available, but there is no guarantee. I know she doesn't want to use one all the time, but trust me if she is having hip problems from time to time at home, the chances of her having them during any given Disney Park death march are much higher.
Disney charges a lot for theirs and they are throttled down to snail pace. You could pay for a week with an outside sourced one and use it or don't, but I won't take many rentals onsite that would pay for the week. The biggest thing about offsite rentals is that if your driving it is a long way to the the parking lot from MK and with a bad hip it can be a pretty painful walk. Same with from the far end of Epcot to the parking or bus location is also a long way. Trust me, from someone that took that chance, if someone has leg/hip pain it can be a pretty miserable day if you don't recognize it's possibility ahead of time. You folks know better about her complete condition than I do, so do what you think best. The onsite rentals cannot leave the front gate and that is also where you get them. A bad situation at the far end of any of the parks can be torture. If she doesn't want to use one due to pride. No one really is paying that much attention and if they don't like it try not to care. They are jerks that have been lucky enough to not have pain at that point, but the level of enjoyment for her can change to great if pain isn't in the equation. It is sometimes a long way to the buses as well and like I said you cannot take their rentals with you if rented at the parks.