well since we're all up for editing & revising what has been said,
I'll give you my version:

"Are you able to watch the kids? If you can't watch them I'll get a sitter, thanks"

Remember "the dance", this is part of it.

She will invariably (I love that word, that and the term 'crap behavior'), ask you what's up and you will just reply "going out, are you able to take the kids?"

Short & simple.

You've made your decision to go out so no need to include her in that part of it, her only choice in any of this is to watch the kids or not and you'll have a plan in case she says no and if she does say no, you will reply "np" (no problem) and that's it.

Short & simple, a little mystery thrown in for color.

Just get an answer from her either way on watching the kids, you are looking for yes or no and you don't have to give her info on where you're going & who you're going with.