Mate, I'm so sorry to hear about what's happened. I can't help with the pain, this is going to hurt, no matter what happens. As others have said, share your love with her while she's here, she may not be 100% aware of who you are, but she'll feel the connection and you might be able to bring a little light into her life.
By the sounds of things the care home option would be best all round. It's nothing to fear, believe me. My dearest aunt lived alone. She was strong, independent, the matriarch of our family. My wife's mother died young, May (her older sister) became the mother figure in my wife's life. She looked after my sons when they were young, she was their real grandmother. She was always the rock that anchored our family.
But then the dementia struck, and she wasn't able to look after herself any more. She lived with us- holidays at first, then for longer breaks, but with the boys in full time education and both myself and my wife working shifts, she wasn't getting much better looked after with us than at home with visiting carers. She needed 24hr care and supervision, she was getting barely a third of that.
It took us almost a year of heart searching and deliberation, but eventually we looked for a care home. We looked at several, only one felt like home. So we bit the bullet and signed in.
May's health and faculties were deteriorating, she really needed 24hr care and only the home was able to give it. She settled there. The constant surroundings and regular routine, the familiar faces and constant interaction, the genuine compassion and fellow feeling the staf have all made her final months the calmest and most peaceful she'd had since the condition struck.
She passed a few months ago. It hurt then, Gods it hurts now, but by that stage she was wasting away and in constant pain. The confusion she felt made things so much worse. But she recognised my wife at the end and drew a far bit of comfort from her being there. Life is cruel, death isn't always a bad thing. I miss her, but I'm glad she doesn't have to suffer any more.
Like I said, show your grandmother love, let her know you care, even if she can't quite remember who you are or what you used to mean to her. And don't forget your grandad! Pop around and see the old fella every now and then. He'll appreciate the company, even if he doesn't say so.
Good luck mate. Take care of yourself and try not to let it get you down. Life is cruel, that's why people are kind...