Had a 19-year old cat. Cat was still with my parents long after my sister and I had moved out. Happened to be visiting, cat was sick but cats get sick, right? We saw her crawling under the stairs, where she never went. Poor thing was so dehydrated, she couldn't move right, her back was having such spasms that she was bent in half.

We went to the vet, and the options were either re-hydrate her, which would buy maybe 2 days because the vet figured her kidneys had shut down--whether that was causal or caused, she was pretty sure. So, there exists cat dialysis, but not in the universe I live in. Option2 was rehydrate her, so she'd be comfortable, then put her to sleep.

It hurt a lot, but it was so obvoious that at least we didn't have to second-guess.

Meaningless co-incidence: this was about 3 days before I left Illinois to go to California.

True that cats hide to die. It might be worth your while to consider euthanising before the cat pines for the fjords in an inopportune location, especially since you have kids.