Oh I am SO SORRY and I do understand this frustration. I cringe with each new kitty addition - with memories of all the cat pee we have lived with. There is still the possibility that Kate had a bladder infection - wait and see! With our last cats, we did have to cut away carpeting and remove pieces of baseboard that smelled the worst. We threw away one chair. The enzyme products work pretty well, but honestly, I know the frustration of never really smelling clean! Our last geriatric died in April and we got two new kittens. After six months with no accidents, we finally replaced all our carpeting and the house smells fresh again. But, I alway wonder WHEN one of them will decide to start it up!
I can't offer much more than sympathy because I really feel the sadness. We love these animals BUT what about when they destroy our homes? It is very hard. If the kittens start ruining the house for no medical cause, I will be tearing out my hair and sobbing again.
Please report back after Kate's vet appointment - maybe they will have some suggestions for you.