the general guideline for cardiovascular fitness is to aim for 150 minutes per week. Since she can walk at 4 mph, she cannot be that de-conditioned. I would do a 1 mile walk test with her to see where she stands. You can suggest to her an interval training with very small increases in incline (which are hardly noticeable), and that should ever time improve her conditioning.
The shoulder problem is of greater concern unless she sees a doctor and/or therapist.
The mere fact that she is 61 does not mean that you cannot train her unless you have a senior fitness certification. You should be knowledgeable to do an assessment and then proceed from your findings.