Do not give your senior pet to an animal rescue. I think the mental anguish they'd experience they'd suffer from feeling abandoned would hurt them so, so much.
Do your best. Talk to your vet and ask for guidance.
We all face this, eventually. It is hard to face that our cherished pet is aging, but it's our duty to see them through.
His mom is in assisted living, not a nursing home. My mom is also in assisted living. She's got a stove in her apartment, she can cook her own meals if she wants to! Until recently, she could drive herself to Walmart if she felt like it. She has decorated her apartment in her own style because--get this--it's her home!!
Plus he hasn't said one thing about pointing a camera at his mother's bathroom!
It is her home. How disheartening to see you think it isn't.