Cheeky,I am not a doctor but have had the same symptoms as you describe. In my case the cause of dizziness and falling are attributed to:
1. Low blood sugar. I am not a diabetic.
2. Very possibly the diet could be causeing the falls due to lack of energy, too low calorie count.
3. Since I have also had this problem, a stroke or TIA event can cause the neuromuscular system to dysfunction and create the same type of symptoms: dizziness, falling over, slurring of words, forgetfullness, weakness on one side of the body etc.
Best recourse, continue to have your mother examined by the primary care doctor and look for the obvious then look for the more involved problems. Check the diet, blood sugar etc first, the problem maybe totally disassociated with the cancer therapy.