My mum was a very independent lady too. She lived for a long time "independently" with dementia, but eventually she could not remember how to use the phone or TV remote, was not eating or drinking properly because she could not remember how to make herself something to eat or even a cup of tea and was going out at night dressed only in nightwear and banging on random peoples doors because she was lost. She too would not accept carers - she wouldnt allow them over the doorstep and half the time wouldnt let me in either! She fought tooth and nail against moving into a care home, begged me (with tears) not to put her into a home and tried to make me promise that I never would. I didnt make that promise as I already knew this was the only option, but it took a crisis to get her there.
Eventually mum had a TIA and ended up in hospital. She moved from there to her care home and lived there for the rest of her life. For the first 6 weeks mum was constantly "packing to go home" - by which she mean that she had pinched a black plastic bin bag and put a few random items of clothing and a few other things (one shoe, a couple of pairs of pants, the top half of her PJs, a hat and a load of tissues) in it. Eventually she settled and amazed me by making friends and joining in with activities, which I would never have believed that she would do. She positively thrived there - regular food and medication did her the world of good, the simple routine and nothing being expected of her gave her security and people always being around, day and night, reassured her. Near the end she said to me "they all love me in here" and she was right - they did.