I'm not (yet) a father and haven't ever had to deal with a situation like this, so take this for what it's worth...
Unfortunately, you're facing a tough challenge if talking to your ex doesn't work. If she can't see (or doesn't care) that her parenting is resulting in rude, inconsiderate, ill-behaved children with no respect for authority, their parents, or anyone else, you're going to have a serious uphill battle. Try talking to her about this (in a calm and rational way) and probably try to keep the discussion in terms of the well-being of the kids, and avoid any issues in your own relationship. Tell her that even if she doesn't like or respect you, it's unhealthy for children to feel that way about their parents, and it's going to hurt them in the long run (in fact, I'm sure it already has - no one wants to have those feelings about their own parent, and I'm sure somewhere behind the "indoctrination" from their mother there's some pain).
Also of course continue trying to set a good example for the kids, and talk to them about it as well. Be sympathetic, calm, and loving. Tell them you're sorry for what happened between you and their mom and the effect it's had on their lives, but that you *do* love them, you didn't "leave" them, and that even though they continue to treat you badly, hurt your feelings, and misbehave, you still love them and want what's best for them.
Lastly, and no offense here, but take a good, objective look at yourself to see if any of the things your ex says about you really are true, as much as you may hate to admit it. There's no excuse for the way she's handling this, of course, but these are very often not as one-sided as the people involved think they are. It's very easy to become defensive and lose sight of the fact that perhaps some of the other person's complaints about you are, in fact, valid. No one wants to face their own failures, weaknesses or flaws, but we all have them, and the only way to improve is to acknowledge them and look them head-on. Again, I'm not trying to accuse you or make it seem like you've caused or deserve this, but if you really want to try and resolve this you have to look at it from all angles.
Good luck with this, hopefully someone with more experience and insight can give you some better advice, it must be a horrible thing to have to endure.