First off, I'm so sorry you're having to deal with any of this, and for what you have had to deal with growing up with that kind of dysfunction.
My own family had all sorts of dysfunction, but nothing to the extent that you've experienced. I found that going to a kick ass counselor helped me formulate my own boundaries and responses to the crazy, and helped immensely with the guilt and obligation part - it wasn't my fault that my family was screwy, and there wasn't a damned thing I could do to change their behavior.
So I say the same thing to you - you only have control over yourself. You can't change them, but you have the power to stop them from hurting you or your own family unit. You don't have to have contact with your mother at all unless you are getting something out of it. Same goes for any siblings. You owe them nothing. Just because some happenstance of birth made you related doesn't mean you have any responsibility for their lives or troubles or have to take care of their messes. And any relative or even friend that uses their relationship to you in order to get something from you - money, power, control, or as a scapegoat - is a bad person that doesn't deserve to have ANY relationship with you, let alone your kids.
The fact that you feel like you are a black sheep in your family for being successful and having your shit together says way more than you think. You should not feel guilty for doing better, because I'm sure you didn't get anything handed to you and you probably worked your ass off to get where you are and to feel good about yourself.
There is nothing wrong in cutting off your mother or a sibling that is a user/abuser. In fact, in the case of a narcissist, that's the best thing possible because they are emotional vampires that will stop at nothing to destroy anyone that doesn't do exactly as they are told. I would not allow someone like this in my home, let alone around any child, since they are not remotely a relationship that needs to be nurtured. I cut off my own mother for about a year (she's a borderline and was extremely verbally abusive) and my husband's just plain crazy mother has been cut off for close to 3 years. I've asked my husband periodically if he wants to renew contact with her, and he says that he's never been happier since he doesn't have to deal with her drama, and can't see any reason at all for inviting the crazy back into his life. And yes, we both went to counseling at several points to work through all of this stuff and the validation that it wasn't us, and no, that wasn't normal was such a comfort (I did joint counseling with my mother, and the counselor definitely though my mother was crazypants).
I gotta say, in your mother's case, she'd be dead to me if I was in your situation. Those are some gross violations of the relationship, and even talking to her on the phone or a card at christmas would be done as far as I was concerned. And the sister - she'd be a hair away from the same thing. I would have read her the riot act that if she EVER did anything like that again, that she wasn't welcome in your life any more.
Ask yourself what are you getting out of the relationship? If there isn't anything positive, then why are you continuing it? If the answer to that is some form of "because it's family" then you need to take a step back and ask yourself, "is this the way family is supposed to treat each other?"
There was an excellent blogger that talks about growing up and living as an adult survivor of a narcissistic mother (she has since stopped blogging, but she keeps the blog active for good reading materials) that you might want to read through:
http://narcissists-suck.blogspot.com/As far as your grandfather, I would take your mother out of the contact loop. She doesn't need to be the gatekeeper and you certainly don't need to be giving her that power. I would make sure you had several different ways to contact your grandfather, and make sure he understands that you want to be told if anything happens, and you would never cease contact with him voluntarily. He must know what sort of a person your mother is, and there has to be at least a few friends that he has that can also let you know if something happens. Establish a routine of contact/visits with him so you won't ever be in a position of depending on your mother for information.
And as far as your nephews and nieces - you do what you can, but ultimately it isn't your job to be their only good example. I understand that you feel sorry for them, but you're putting too much pressure onto yourself to think that you can or should be there for them more than you are right now. If their own parents aren't good role models, it's still possible for them to turn out okay - you yourself are a prime example this is possible - but they will have teachers, friends' parents and other members of society that they'll come into contact with that can guide them. Don't try to take on the responsibilities of the world on your shoulders.
I have a feeling that you were the "responsible" kid growing up, and this has caused you to continue that role as an adult. If you don't help out or do what is demanded, there's a sense of guilt or anxiety since that was the role you're supposed to fill in your family. Step back and take a deep breath and start seeing that you don't have to be the glue to hold this mess together - you aren't responsible for all of this and you need to put yourself, your child(ren) and spouse first and do only what you feel good about doing.
And I wouldn't even get into the correcting the lies part of what your mother spreads about you. If they aren't completely stupid, they have an inkling that your mother is poison, and if they believe anything she says about you, then they don't know YOU that well. In which case, I'd say the only defense would be a simple "Wow, well, I guess her saying something mean about me is expected, but I'm sad you think that's true." Works for just about every situation.
And don't let them guilt you into doing things or putting up with things you shouldn't - you are NOT being the bad guy trying to extricate yourself from a toxic family situation. You are a strong, capable and successful adult. Find your spine and stand up for yourself and your own family and don't let them drag you back into that mess. State your boundaries if you're wanting to still have contact and also state the consequences for violating those boundaries. And then stick to them.
Your life will be so much better if you don't have to even deal with the crazy - or can make sure that the crazy isn't going to be tolerated (hanging up on ranting mothers is scary at first, but the adrenalin rush after and the fact that they learn to STOP THE RANTING if they want to talk to you is priceless!)
If you haven't already considered this, I'd recommend counseling as it was one of the big keys to dealing with my own situation. You need validation that your relationships are not normal, and that it is okay for you to enforce your boundaries, and the right counselor can help you work through all of this (some counselors aren't a good fit right off the bat, so make sure you feel good working with them).
Big hugs, and good luck working through this.