Re: Moving after divorce with a manipulative ex wife.
Andy, I'm not familiar with your back story but it seems fairly evident from your thread that you aren't totally over your ex-wife, and that it may be too early for you to date and certainly too early to be jumping into bed with random women.
I went through this kind of communication thing regarding the kids with my ex-husband after my divorce, and I can promise you that it does get better. Right now she is using the kids to jab at you and irritate you. And you are worried about things you can't control (ie, her boyfriend and relationship with him). You two are poking back and forth at each other because of the residual resentment, anger, etc from your past relationship. Your focus is on your kids, but it's also on her. What you have to do is take her out of the equation.
I think you should take the advice of others and stop asking her about how the kids are doing. Buy them phones. Be clear with them how you want to be available for them anytime they need you. Unless there is evidence that she is abusing them, you can't control what she does with them when they are with her. Nor should you try. You CAN control what happens when they are with you.
Yes, it would be nice if she prioritized the kids such that she would offer you information as to how they are doing, especially if you don't see them often. But the fact is that she isn't required to, and this doesn't always happen after divorce. You just have to work to find ways to leave her out of it and find out directly from the kids how they are doing.
As YNot said, though, I think you should look in the mirror and really think about why you are interacting with her in these ways, and what it is that you truly want to happen. You need to take her out of the equation, but I'm wondering if you are really wanting to do that.
Don't let people become a priority in your life when you're just an option in theirs.