I have a question: Is this exchange on Tuesday nights actually part of a fairly negotiated parenting agreement, whether tentative or final? Or is this just some demand your H is forcing upon you through guile and coercion, something you have yielded to in lieu of a definitive argument against, even though your gut feeling is telling you to say no -- but you're trying to be nice and keep the peace anyway?
See, Karen, your H is a bully and he is the sort who will use any means he thinks necessary to get what he wants. (I guess I don't have to tell you this.) If he is due the Tuesday Night thing, and you've agreed to it, other than being coerced into it, I would say that's one thing -- meaning you should honor that. But if he's just preying on your good will to finagle more legally-advantageous time with the kids, then it's time you tell him to back off.