Your mother will certainly be able to have radiation treatment, but the real question you need to ask the doctors is will it help with the dizziness or the hearing loss?
If you read about peoples experience with radiation, it often comes with increased balance problems, and hearing loss.
Eventually the problems stabilize but at 89 her ability to recover will not be as good as a younger person.
Clearly we are not doctors and cannot provide advise, however based on my personal experience with a small AN, hearing loss and balance issues and radiation treatment I will say the following.
Knowing what I know now.
Would I have radiation again at 46 years of age. Yes absolutely.
Would I have radiation at 89 years of age, for a small non growing AN. No
My concern would be that the increased symptoms typically caused by radiation, would not diminish in time, for me to have any improved quality of life.
The short term pain of increased symptoms is typically two years for a much younger person.
My balance was poor, for a few months post radiation.
At 46 these balance problems were inconvenient.
At 89 I reckon the balance problems would be frightening, the risk of a fall, a hip fracture, I suspect would be high if your mum felt the way I did.
So as Jim said we cannot give advise, and we are not doctors.
However based on my personal experience at 46, would I do it at 89 no, I would remain in watch and wait.