Honestly, I wouldn't even explain myself even that much to her. I'd say contact via phone only and she knows the reasons why. If she says she doesn't, I wouldn't invite confrontation by rattling off all her transgressions... It shows her that you're still keeping track of her, it validates her and it validates her behavior. If she's trying to get attention, she realizes her behavior has worked. I'd just let it go.
If she bullies the kids, honestly, I'd let her know that she's not to do that and, if she persists, I'd bring it to court or mediation, get that using the kids as an intermediary is forbidden. If you've already done that, I'd then go to court to declare her in violation. It's a hassle and an expense, yes, but I suspect it'll be the only way you can get her to take you seriously and the only way to protect the kids. And, correct me if I'm wrong, but I seem to remember you being OK with taking those kinds of steps to make sure they were OK.
As to her working, I'll tell you now... That's a battle best given up now. It's one that we fought for years with my other half's ex. You can look to motivation, but in the end the motivation is probably nothing more complicated then laziness. The fact that many states reward this laziness by asking the child-support paying partner to make up the difference in the lack of income certainly doesn't help. Especially if you're ambitious and career motivated, hearing the complaints about her working, or the lack of it, or her financial problems will only make you insane and she'll never, ever, ever aspire to do anything better with herself because there will ALWAYS be a reason why it doesn't work.
In the end, if she chooses to not work and suffer financially as a result, that's something she has to be responsible for, not you. As long as you've gone to court and gotten what you pay cemented, the best you can do, very, very unfortunately, is hope at least some of the money is getting to the kids. And let me tell you, I KNOW how bad it sucks... I really do. I know how hard it is to keep being civil about all of it when you pay that money and hear that, despite having no issues finding the time or finances to go out to dinner and the movies or finding the means for a week long trip to Disney or going shopping for various unnecessary things, you hear from the ex (or even worse, the kids), that the power was shut off because she hadn't paid the bills in months... Which is what happened with my other half's ex... And knowing that even that doesn't inspire any other sort of motivation to work more.
I know I have a lot of issues and have a hard time being nice about it, sometimes moreso then my other half who has to actually restrain himself from going off, as I work 12-14 hours 6 days a week and, as a result, we're just about free of debt, save for the credit card from his marriage that went to her expenses as well, and have a great savings account... And I'm totally and completely incapable of understanding why somebody would remain intentionally under employed, especially when they have kids. I don't have a single concept of why or how one would be OK with that level of complacency.
So... As you can see by my rant, it's a frustration that will never go away... I'd let the work thing go. If it gets in the way of her ability to properly take care of the kids, go to court. But otherwise, telling somebody with no ambition or desire beyond catering to their own laziness to work harder is like yelling at the clouds to stop raining. Find satisfaction in looking at her and knowing you're the complete antitheses of her and that your ability to work, sacrifice, and provide for the kids and not your own personal satisfaction makes you the better person.
And, for God's sake, reinforce with the kids how important it is to work and sustain themselves, less they get caught in the same cycle she is when they are adults as they saw nothing better.
