@SweetChilliGirl she is of sound mind, you say. So if she truly thinks it's the best thing for her to go home nobody can stop her.
I suspect it's "just talk", like when we say, "I want to kill so and so". It's a way of expressing her (quite understandable) disgruntlement at her current situation.
If she gets a care company to assess her needs and arranges a contract, sorts out a taxi home, rings the GP surgery and books DN appointments to change the catheter, maybe she really meant it.
Otherwise, either she didn't mean it that much, or she would struggle once home.
You can sympathise with her without saying you think it's in any way a good idea!
Even if she did get herself home, IME what care in your own home looks like has its downsides. I would not blame you if you reminded her of them...
Live in carer - what if you don't get on? House share with (initially) a stranger.
Carers coming in? Timings are off, rotas wonky, why is Michael doing a breakfast or bedtime slot when I only want personal care from women?
Endless microwave meals. Sweet but gormless youngsters who can literally not even boil an egg. Food in fridge not being thrown out in a timely manner. And at night, you're on your own. And you have to do online shopping, sort a cleaner to come in, fix the house.
Care homes ain't perfect but you get cooked meals and get to see people who aren't your carers, and usually they have regular GP visits so you can get seen rather than phoned.
As you may realise I have considerable sympathy with your situation ♥️