This is a great thread, alot of us go through this in one respect or another with an aging parent.

A geriatric care manager could help
But I think you need to read up on ways of talking to parents. The interactions you described make me understand why you mom is defensive
You could have been a lot more gentle, "hey mom, have you noticed the water in the kitchen? What do you think ?" Etc rather than announcing that you had decided there was a problem and that you were calling three firms.
You can get to the same result using conversational approaches that preserve parents' sense of autonomy....

OP,I did not read all the responses. Yes, a geriatric social worker would really help. I had a geriatric social worker for both my mom and dad. Is it something you can afford on an ongoing basis? First you write about what you think the problems are and then the social worker does an evaluation. It is so long ago, now I don't quite remember how things worked. But I had one visiting mom and dad twice a month for years.

Your mom sounds like a prime candidate for assisted living, OP. Start lining up possibilities and be ready to push when the next crisis hits. That sounds cold, maybe, but from what you describe it also sounds like what the situation warrants.