Oh Janice,
You do sound desperate indeed, and desperately worried and sad. It's with some sadness to have to have to say that what you, your poor mum and your family are going through is common. This means that so many have to go through the heartache and tears to do the right thing for the safety of a loved one. Not being alone in this won't help you right now, I'm sure, but at least you know that many of us have been where you are and have allowed time to show us that it (usually) works out ok.
I remember leaving mum at the Nursing home and having similar feelings to when I left my little ones all on their own at school for the first time. The confusion on their faces, the pleading looks, the tears. I don't know how my heart hasn't broken in two with 3 little children and my poor mum, but in time any situation can be resolved for the better.
I do agree that bringing her home might be a knee-jerk (and completely understandable) reaction, but it may not be the best one all round. The pressure on your family and any paid carers would be immense, particularly after reading how your mum has been recently. I can understand that by her being home, there's a tendency to believe (to WANT to believe) that in her own environment she won't want to wander, but it's a very big risk, despite maybe being partly true.
It will take time to build a trusting relationship with the home and (like with school) you are handing over your precious loved one into someone else's care, so it's important you find someone there you get on with and can speak to often. It may give you peace of mind to put together some notes to hand over to the home, with details of your mum's likes and dislikes, perhaps some topics she might engage in over a chat. If the staff have something to occupy her when she's agitated, she may calm down without the need for any medication.
It will be therapeutic for you too, to be able contribute something at a time you must feel so helpless. Write about favourite holiday destinations, pets, favourite music or films, tv programmes...anything the staff can talk to her about. Also include a bit about the woman she was, before dementia so that they can tap into her history.
They will be trained on how to settle a new resident, and no matter how hard this stage will be for you and your family, if it's a good home, they will manage well. But it takes a little bit of time.
Do keep posting and we will try to reassure you, as you come to terms with such a difficult time. So many of us have been there, and many are there now. It will get a little easier, I promise.
Stay strong, and know that she is safer there than anywhere else right now, and that can be your focus over all the horrible emotions that you have to deal with. She is safe, and cared for.
Lots of love,