Hello and welcome to TP, Portia.
The requests to "go home" are very common in persons with dementia. Even people who are at home, will ask to go home. I'd be willing to bet many, if not most, of us here on TP have heard this.
What works best for my mother is an approach to minimize anxiety and distress. Often that is trying to address her emotions and the feelings, behind what she is saying, and offering reassurance: you have a place to sleep, you can stay here tonight, I will take care of it, you won't be alone. Sometimes it's redirecting: what do you want to do at home, who will be at home, and so on. Sometimes it's part of sundowning. Sometimes I offer a reason why she can't go home right this second: the roads are bad, there is snow and ice (a deterrent for her), and so on. Shifting blame is also a strategy I use: the doctor wants you to stay here for a while, to build up your strength.
I know some are uncomfortable with lying but realistically for me, I always take whatever approach will cause the least harm and distress for my mother. If I contradicted her and told her the absolute truth, or tried to argue or even discuss things with her, it would upset her and maybe even trigger a catastrophic reaction. I see no point in that, and in fact, in her situation, it would be unkind or even cruel.
I'm not saying this is what you should do, we all have to find our own way. I do think it can be helpful, as carers, to think about what we are trying to achieve.
If you've not seen the compassionate communication documents, they can be helpful and we can post links. There is also information on the Alzheimer's Society's website that may be helpful for you. Best wishes.