OP, since you know that this person brings her kids everywhere, and since you (I assume) don't want her to bring her kids on this occasion, I think that you are still being too coy. You are assuming that she will pick up on the "no kids" vibe... however, I think that that is really unlikely given the back story that you shared.
I think that this is an occasion where you need to clearly spell things out. Here is how I would reword your email:
"CRUD MONKEYS!, I am so sorry, I just realized I forgot to include your email address on this email.
Mr K and I won't be bringing Little K along. We're want a fun night of grown up conversation, without any kids there to distract. I hope you're able to make it, but I understand if you can't come because you would rather not leave your kids at home."
I like this wording.
Ditto. Because it specifically says, "if you can't come"--it lays out that other option.
You could be even clearer: "We're organizing a grownups-only get together. If you can find a sitter, we'd love to have you come."
Feel free to add stuff like: "I'm so hungry for conversation with people who are taller than 3 feet!" or "I need grownup time and grownup conversations--maybe even with swear words, LOL!"
Even, "I've gone to great lengths to secure a sitter, even though our usual family members aren't available. That's how important it is to me to get away from the 'mom of little kids' vibe. If you and Hubby can find a sitter, I'd love to see you. I miss being a grownup with you!"
Tell her what you want, what is important to you: "It's important to me to be with only grownups. It's so important, in fact, that I spent a lot of time finding a non-family sitter so that I can do this."
I think you can even say: "including your kids would completely change the vibe, so if you can't find a sitter, we'll have to get together on our own some other time."