I don’t deal with unsealed sources of radiation, so my first advice to you would be to follow the instructions given to you by the hospital. I-131 is primarily a beta emitter (radiation dose due to electron emission, short range) so the primary exposure mechanism of concern would be ingestion, i.e. physical proximity to your wife is not a significant issue. Keep bodily waste contained and dispose of as instructed. The effective half-life is about 5 days (biological and physical decay) so I would think that you would have been told to take precautions in handling wastes for a couple of weeks.
The waste goes into a 2000 ML drainage bag then into the commode and in the septic system. The other I'll bag up and take outside if I can keep the wildlife away in the process.