I’m glad your wife is getting the treatment she needs and has such an excellent caregiver! Best wishes for her recovery.
We had a cat that underwent thyroid radiation treatment. We were told to use gloves when we handled her litterbox, etc, and to wear gloves when petting her, and then dispose of the gloves. We weren’t allowed to have her on our laps or hold her for a few days (how many I forget now). I would think that the litterbox issues would be similar to handling her waste bags, etc.
My suggestion is: For tonight, wear gloves and try not to cuddle up. And then tomorrow bright and early, call her doctor or the hospital or both and point out that you have *special* issues because of her disability, and you need precise instructions how to handle it. The hospital probably has some sort of protocol worked out for this already, to keep their own workers from being exposed. You just need to find out what that is (and also find out if you need any special equipment).
As for the doggies, call your vet. Lots of pets undergo this thyroid treatment now, so your vet ought to have useful insight into how to protect your pets when they come home.
Best of luck!
I'll see the Vet tomorrow picking up some meds so I'll see what he says. So far we've been told a week by nuclear medicine at the hospital.