dancingstar I think you've got a few things on their head here.
Your mother has a pattern for many years of being ill ( the PP who said he's 80 and may often be ill clearly didn't read that bit). So you have to take the long view, while accepting that she may genuinely be ill. It happens at 80.
She's playing the Tug For Attention game in spades - what, your brother goes out for a few hours and she has to get ill? every time she can't get you even for a few hours, she's ill? For years? No, this isnt illness. This is uberneediness and controllingness.
Now she's entitled to some attention and love, yes. Every half-way decent parent is (though some don't even quality as half-way, sadly). But not to dominate your life.
So a couple of calls a week seems fine and the odd visit if she's 300 miles away. And like PP's said, say that you're keeping the phone off the rest of the time. Just don't answer.
Beyond that, every time she says she's ill, tell her to ring the doctor (sorry doctor!). If it's an emergency she can ring 999 as she did. I'm sorry, but the relatives will very soon get used to her ringing them up and telling everyone she's dying - 6 times a month. I've been in your shoes, people get wise very fast, except the poor schmucks who are immediate family to the oh-so-ill person. You are showing your love and concern by ringing twice a week.
I would strongly recommend talking to your brother and sister about this and telling them you've going to take a different approach. If they're willing to go along with you and take the same approach, your mum is going to learn quickly that pulling the illness card won't work. Because that's what she's doing, pulling the illness card.
I think I must be such a selfish cow - I hate myself. Firstly, don't hate yourself, please. it doesn't help solve the problem.
Secondly, no, you are doing everything reasonable and over and above that.
Thirdly, actually its your mother who is being selfish. No reasonable and generous person expects their nearest and dearest to be absolutely at their instant attention 24/7 (which is what you are). That is selfish behaviour.
People often act like this when have learned that they can't ask for a reasonable amount of attention or to have their needs met. Has your mother been sidelined / had to put others' needs first for a long time at some point? People often develop these weird and unhealthy ways to ask for attention when that's the case. Mind you some just get like that anyway! Just askin' really =)
Again, it is reasonable and right for you to have your own life and to not be contactable for some hours.
Essay over :P