When you say mom has a low carb breakfast what does she usually have? It's much easier to see where problems may be, with a menu. For ketones, if you go to your local Pharmacy you can buy Ketostix, they are not expensive, and she can test to re-assure herself. Ketones and a high BG is not a good combination, it points towards Ketoacidosis which is very dangerous. I always have ketones, but mine are dietary and very safe, and I want to see ketones when I test.
Please let us know how your mom gets on, it's such a worry isn't it?
Take care - Jo.