I would defintely put my mum in a home if she became incontinent. However, potentially all of my cats pee in the house - Seth & Sammy partly because of a past trauma, Charley because her last owners never house-trained her (although she is now housetrained she uses it to make her displeasure known e.g. about the weather, the new dog etc etc), and all of them because the last owner of the house had a cat that peed EVERYWHERE and we still haven't quite managed to get rid of all the carpets/flooring and we'd have to completely replace the kitchen.
Result - every morning I patiently clean up whatever mess I find (nowadays it's just in the kitchen), without shouting at the cats. In the Winter we bring the litter try into the kitchen so they don't have to go out. And we've shut them downstairs until they settle down - although they're allowed upstairs under supervision, just not while we're out). Certainly wouldn't have them PTS because of it, and definitely wouldn't put them up for rehoming, they're my babes.
Grrrr... hope your day gets better Elaine...