I think Sugar's advice is spot on.
What stood out for me was your last sentence, 'I am sure she wouldn't be any happier or live her life if we moved to be with her' - no, she wouldn't. She could be a lot happier right now, by trying to socialise, take the doctor's advice - but she doesn't want to. She is a wallower and she'd be exactly the same if you lived together and gave up everything for her - it's who she is. Or who old age has made her become.
Your mum sounds exactly like my gran - my mum (and all of us) have had years of this. She lives locally to them, so caring isn't a problem fortunately. But on an emotional level, she is horrendous. Her (minor, given her age) health problems are a constant refrain. She literally cannot talk about anything else. Like yours, she is lonely, but has few friends, largely because she has become increasingly negative about every single thing in life. The irony is that she was a vivacious, enjoy-life type of person - but unfortunately ultimately one who has changed dramatically on getting older. She is a martyr to herself. She sucks the life out of you. I love her, but phonecalls take a bit of gearing up to, shall we say.
The thing that makes my gran so wearing and drives people away is that nothing is ever enough. Any and every topic of conversation becomes a complaint about how badly it affected HER, or a bitch about how much easier that other person has it - not like her 'not that I complain, you know that, I never complain'. Any suggestion for fun, activities, etc. is met with how she can't do x because of her health. She is a black hole of negativity.
It takes a while I think to realise that with people like this, they are actively CHOOSING to be the way they are. It's harder with the old as we can see that yes, they do have so many difficulties to contend with - loneliness, frailty - so to be angry or to criticise them feels heartless. But you have to judge her as a person as well as a helpless 'little old lady'. What is she actually doing? Manipulating you. Refusing to take medical advice, making herself as you say deliberately dependant - all to get what she wants, which involves your entire family uprooting your lives to make hers better.
Don't ever have her to live with you. It won't change her, but it will make all YOUR lives much harder and you would resent her horribly...as would your children.
It's a terrible bind to be in, but from what I've seen in my own family, I can tell you that the guilt should NOT be on your side - I hope this helps. It's only in recent years that my mum has begun to disengage more, as she has seen that as SHE gets older, and has more health issues, her mum's response has been shocking - no concern for her daughter...it just continues to be all about her. It's really opened her eyes to the extent of her (unconscious, undeliberate) selfishness. It's very sad.
You could try pointing your mother's attitude out to her. Next time she suggests a move - 'What would be the point Mum? There are lots of things you could be doing now to make life better and you won't, so why would it be different if we were there? When you won't even listen to the doctor, it seems you're determined to make life harder for yourself - I don't think I can help with that.'
On a practical level, any suggestion that you move should be met with incredulousness. What, uproot the entire family, jobs, schools, everything? If anyone moves it should be her - closer. Not into your house, which is late nights, childrens' friends, noise. Sheltered accommodation a couple of miles away perhaps? As she gets older, it might prove easier to have her within distance. This ONLY works if from the very start you have an extremely busy schedule and set times to spend with her. What does your brother say, is he local to you?
I don't envy you!