As someone who has knee issues due to skeletal problems, drastic level changes are difficult. Turn might also be a problem, particularly fast turns.

Encourage her to do as much leg strengthening as she can. If she can't do squats, there are alternatives. Joyce Vedral has a workout dvd aimed at older women called the "Cougar Workout" which has some alternatives to squats.
store.joycevedral.com/product...eks.html
She'd have to ignore the rather silly chatter but the information is solid.

Not know the exact nature of the back problem it is hard to say but usually strengthening the abdominals will help with back pain. If she is unable to do abs on the floor standing lower ab locks, rolls through the three sets of abdominal muscles, and knee lifts using the abdominal area are all effective. Obviously, the pace and emphasis on correct and safe technique would be very important.

Good luck to you both.

What specific injuries does she have?

All you can do is be sure she has warmed up and stretched, and try to get her to keep her posture as close to correct as possible. The rest is up to her. She may benefit from massage therapy, physical therapy, Feldenkrais, Alexander technique or various other methods, but that has to be her journey. I have found that body awareness is a huge factor in recovery. I feel that it is very important to develop body awareness, not only for those trying to heal, but for those who have not yet been injured. It helps you stay healthier and when you do get hurt, the awareness is already there so you can work toward healing right away instead of having to learn the awareness part!
One thing to do is to lie down and very slowly move your limbs in your range of motion and note every little place that is tight or painful, or does not have smooth movement. Those are the areas that you want to very gently work on by moving yourself to those points and being very aware of them. Do not move to a point that it hurts, but to the point that you are aware of the spot. Try it on yourself. This is entering the range of therapy, so probably should not be done in class. I explained this very simplistically so that you can play with the idea. A therapist would lead the person in a more detailed approach. It is not recommended that dance teachers do any therapy unless they are indeed therapists, of course. See the "cover your butt" sections!