I think your "so called" friends at work may have a point. Management is aware of the situation and unable to resolve it. You like your present situation enough to stay so, s*ck it up (hope I'm not being to blunt). Your in an imperfect situation that's not going to change. Do your work, take up the slack on her's, and management may well recognize you for the extra effort. She'll retire eventually and you'll win favor with your superiors. My two cents.
If one person in your team isn't pulling her weight and is a negative influence on morale then it's your manager's job to sort her out. So I think you should take your problems to your supperior.
The thing is that work-place friends aren't necessarily real friends because your relations with them are ultimately built upon a professional relationship, and part of a professional relationship is the knowledge that you are managed by other people.
So while it might be off to run to mommy when you're dealing with normal friends, in a professional situation there's nothing wrong with it. You owe it to yourself and to the people who employ you to try and get the problem solved.