Don't give in to your ex, you'll just give credence to her belief that she can get away with messing up her own life constantly and you'll always bail her out. Seriously, don't do it. If you get involved at all, make sure anything you do and anything you pay for DIRECTLY benefits the kids. Don't let her blackmail you. If you have to, take her to court on the grounds that she's not mentally stable enough to be a parent, although I would only suggest this as a last resort to save the kids.
She only contacts you when she needs help. You're not her dad. Let her know you will not tolerate this poor treatment of you and your loved ones, and that she has no right to trash-talk the people you care about after walking out on you. Take no crap from her. Say you'll help the kids, but that she's an adult and must take care of herself.
That's just my opinion, anyway. I've got some messed up people in my family, and the thing I've learned about them is they typically don't change. Manipulators (like my aunt, who would cozy up to people and then treat them like slaves) will continue to do this as long as they can. If you wise up and say no, they'll get angry. But so what? Better to move on with your life than let these types of people poison it.