This is a difficult one - I can tell you that at present we do not have enough research evidence to decide whether surgery or conservative treatment (physio, injections, medications) is the best option for rotator cuff tears.
I have copied and pasted the "plain language summary" of the latest Cochrane review below (this is a very high quality review of all the research in this area).
Coghlan JA, Buchbinder R, Green S, Johnston RV, Bell SN. Surgery for rotator cuff disease. Cochrane Database of Systematic Reviews 2008, Issue 1.
This summary of a Cochrane review presents what we know from research about the effect of surgery for rotator cuff disease.
The review shows that surgery may not lead to any difference in pain compared with different exercise programs.
There was not enough information in the included studies to tell whether surgery would make a difference in the ability to use your shoulder normally, your quality of life, your shoulder's range of motion, your strength, the chance that your symptoms might come back, the time it takes to return to work or sports and whether people are satisfied with surgery. Side effects that occurred in the studies included pain, infection, difficulty moving the shoulder after the operation, wasting of the shoulder muscle, and the need to have another surgical procedure.
It would be of benefit for your mother to have some imaging done (MRI or ultrasound) to gauge the actual amount of damage to her rotator cuff (full thickness or partial thickness tear), which may help with the decision making. Clinical tests that doctors or physios do give a less reliable estimation of this.
If pain is limiting your mother's ability to participate in her rehabilitation an injection into her shoulder may help - injection combined with excerise and manual therapy generally has as high a long-term success rate as surgery for these kinds of shoulder problems. However the exercise rehab may take quite a few months as the muscles will have wasted and weakened a lot - remember your mother would have to do this exact same (or even tougher) exercise programme after surgery. It really is worth trying the non-surgical approach for 6 months, and re-assessing at this point.
Best of luck to her!