Hmmm I don't know. I've cancelled appointments for my FIL before now (or rather rearranged them) because they weren't convenient for me (and as I'm the one who takes him, they have to be convenient) my FIL is also smelly... I don't live with him, but I change his bedding about twice a week, and I clean his house, wash his clothes AND chuck him in the bath when he comes to ours (about once a week) yet he is still smelly. If he lived with us, he'd probably still smell of old man.
I do not want my FIL living with us, because it would be ME who would have to give him 24hr care and I am not prepared or qualified to do that... especially when the care gets more personal. Its a huge ask for any child, let alone a child-in-law!
I think sheltered housing is probably long gone isn't it if he cannot look after himself in even a basic way? If he needs washing, feeding etc., then maybe a residential home is the 'best' option for him?
I will say that its very easy to criticise from a distance, when you're not the one doing everything, its very easy to get angry. Your SIL may not be doing anything wrong, maybe she didn't realise how cold it was in the house (maybe your FIL turned the heating down?) maybe she was due to go shopping? Maybe the fridge hadn't been delivered yet?
Is you FIL contributing towards the rent? Has the money he's given her been spent on things for your FIL? Is he really being neglected whilst your SIL spends the cash on herself? (Buying a TV really isn't an indicator).
When you choose to allow one family member to take over the care, things can get very VERY tricky, because you all care, but you don't all do the 24/7 caring and that is very different.
Would your DH take on that role? 24/7? Or would it be left to you? Your question shouldn't just be about whether you want FIL in the garage or not, but whether you are prepared to care for him 24/7, its a hard job, and whatever anyone says (and they will all say you won't have to do that) you will end up doing it.
I'd look at residential homes. With a supportive, loving family, sometimes they are the best option all round, you would not be 'dumping' him, you'd be giving him the right care, company, and comfort round the clock.