I really do sympathise - everyone always bangs on about family being the most important thing, the only constant, and it really makes you feel like you've missed out on something profound if you're unlucky enough to have crappy parents. But some people just won't ever change, and if they're not prepared to even try and all they ever do is cause you pain, then they don't deserve to be in your life. There are other people who will love you because they want to, not just because you're they kid and they have to. I'm a huge believer in friendship and, to be brutally honest, if I never saw my family again I don't think I'd care that much.
I think it's admirable that you put your children's right to see their grandparents before your own issues with them. But if I were you, I'd have a word to your mother and let her know that it's a privelage, not a right (I'm fairly sure grandparents have no legal rights), and that if you EVER hear that she's been dropping snide hints to your daughter about you, or trying to make trouble in your relationship with them, that's the last time she'll ever see them. I was turned against one parent by another as a child, and it's only in the last year that I've begun to question what really happened - I'm 23, have been all grown up for years, and it's taken this long for me to wonder. Kids are so impressionable, and the things we're told in childhood run so deep, that it could really cause damage if she's allowed to say what she likes about you to your kids. They could even end up running to her when they're teenagers, and the inevitable problems arise. I don't mean to sound like I'm fear-mongering, but I really recommend being careful that she doesn't come between you and them.
I seriously think that getting out and meeting people would help you a lot. I spent the day alone yesterday, and with friends today, and the difference in how I feel is astounding. Mother-and-child groups, hobbies, anything that gets you out and interacting with people. Are you religious at all? If so, church may be an idea - I think they do lots of things you can get involved in. I've never attended one, but people I know who have always seem to have something to do! What are you interested in? I'm sure there's something that would help you make friends. It makes such a difference to me, maybe it would to you too?