Advice from me?
Well, I'm a novice at all this and at the moment I am hoping to keep my mum at home as long as possible. We haven't even had a diagnosis yet, so I have absolutely no right, no experience, no evidence to even suggest a solution for you. Except that my aunt had AD for 12 years, it developed very rapidly, my cousin never married and lived at home. His own life was taken over by his mum's condition. He didn't even try a couple of weeks respite care to give himself a break.
Have you thought of that? You might just need a break to recharge your own batteries, go out for the day with your children, have a long soak in the bath? A meal out with your husband/partner without worrying about mum. You might then feel you can cope for a while longer.
I would say, but do accept I have no right to say anything, that if someone reaches the stage of saying they can't cope, and is considering the care home option, then it is time to seriously consider it. Put the wheels in motion at least. It could take ages to find one you like, or even to find one at all - in my area there IS only one and the waiting list is tremendous - and even longer to arrange it all.
A live-in carer SOUNDS a good idea - but is it really? My mother in law was physically disabled for many years, and it was something we considered. She had a big enough house to convert the top floor into a self-contained (small) suite for such a person. But we decided that choosing the right person would have been beyond us, and would have created more stress than looking after her ourselves. Plus, a live-in carer needs to sleep and have time off. She wouldn't be working 24 hours a day. As it happened, she had a severe stroke before we needed to make that decision, and died about 2 months later still in hospital. No, you would be constantly checking up that the carer was doing the job, that your mum was happy with her being there, and you'd still have 2/3 of the day not covered.
If it is genuinely getting beyond you, accept that you have done your best. You cannot do any more. It's about compromise. Your children have a right to your time as well as your mum. Make sure she is safe and happy, and make the decision with the best knowledge that you have.
What a painful time it must be for you. Do let us know what you decide, cos one day we will all be at that stage, and when you are on your own it does help to have other people's experiences and feelings to draw on.
I wish you well in making your decision. Much love.
Margaret