This is from:
http://www.thyroid.ca/Articles/EngE12A.html Information is from the Thyroid Foundation of Canada.
Is the Treatment Safe?
This form of treatment of hyperthyroidism by radioiodine has been used routinely for more than 35 years on well over one million patients in the United States alone. Many studies of people treated and examined at a later time show no harmful side effects or complications to the patients or their offspring. Radioiodine is now recognized as the safest, least expensive, and most convenient and effective treatment for hyperthyroidism. In the United States approximately 90 percent of hyperthyroid patients are treated with radioiodine.
My side note: From other readings, it appears that the radioactivity of the feces will be at such a low level that it is basically a non-issue.
Honestly, if you have the money, I'd go for it. If it's going to be at all a financial hardship, though, that's where I'd stick with your last option and give her the best quality of life.
Best of luck to you and Kitty.