Hello, and I'm so sorry to hear of your situation, your mum's dementia, and your current dilemma. It's just not easy and it's so difficult for you. I hope you are able to find some good advice and support here on TP.
Dementia is an awful disease both for the people who have it, and their carers and families. It also doesn't come with a crystal ball and there is no way of knowing what will happen. Your mother could go home with a care package and be fine for many years, or fall and break her arm tomorrow, or need to return to a care home within months, or not. There's just no way to know. All you can do is make the best decision for you AND your mum for right now, with the information and resources you have right this minute.
My own mother is much better off in a care home than at home with carers because 1) she wouldn't accept help; 2) she is not only safe but has company 24/7; at home she was isolating herself and often saw or spoke to noone for days and 3) being relieved of the burdens of everyday living has made all the difference to her. Your mum is not my mum, of course, I just wanted to point out that I would never have guessed how stressful being in her own home, was for my mum. My mother is also, by the way, mobile, very intelligent and verbal and "presents" to most people as though she doesn't have dementia. She will tell you things at home were fine and she wants to go home and live her life the way she chooses, and she sounds competent when she says this--but it is not true.
The hospital did an assessment and determined that she needed 24/7 care, could not manage her finances, could not use the stove safely, could not drive, could not manage her medications, et cetera. I am in the States so our system is different, but this was a big relief to get "official" confirmation of what I'd suspected and now know to the be the case. My mum, who was "fine," could not pay her bills, shop for groceries, cook, wasn't eating, wasn't washing or doing laundry or changing the bed linens, wasn't cleaning and dealt with the mail mainly by throwing it all away or by putting it in piles on the floor. Her home was filthy, she was taking her medications erratically, if at all, and she ended up in hospital after being found wandering, bruised, disoriented, and out in the cold. She'd given her credit card and bank/debit card numbers out over the phone to "charities," written large checks to another charity, and the list just goes on.
I don't want to worry you, but you will need to have a system in place for your mum if she does return home. The dementia will only get worse over time, although of course you can't know how fast or how long. Having a carer in a few times a day may or may suffice for now, but almost certainly will not in the long run, as your mother's condition deteriorates, mentally and physically. Safety is the number one priority, followed by other practical considerations such as medication management, nutrition, laundry, cleaning, shopping, errands, financial management, transportation, socialization, bathing, and so forth.
I do not mean to sound as though I am trying to influence one way or the other, just that you should take a clear, hard look at the facts before you make a decision. Perhaps there is information you can get from the hospital stays and care home about what her needs are, and the best way to meet them. Also, do not be afraid to consider how this is going to impact your life. Unless there are other family members to help, and maybe even if there are, if you are going to be the carer (hands on and/or legal/financial management), this is a big impact on your life.
Best wishes to you and your mum.