Call Amanda now. Remind her that the party is no kids. Tell her now that kids are not allowed and if she can't find other arrangements for her kids, you're sorry you won't be able to see her.
Is your party announced on FB? Write on the wall for the event (or send out a mass email) reminding everyone that once again, kids aren't allowed under any circumstances.
If she does show up, meet her at the door, with a script. "Oh, Amanda, how nice of you to stop by to say hi on your way...where are you going again?" Because obviously if she has her kids, she's just stopping by for a minute or two, you did say no kids. If she says this is where she was going, smile kindly. Laugh, if you can force one. "Oh, Amanda, I'm sorry. This is an adults only party, didn't you see all the posts about it? If you can find someone to watch the kids you're more than welcome to drop by later, though."
If the kids are old enough to understand they're not welcomed when they're turned away, they're old enough to understand that they're not welcomed when they're the only kids there, too. You're not doing them any favors by bending to Amanda's wishes and letting them come, they'll just be learning that you can do whatever you want no matter what anyone says.
Are your mom and Amanda's mom going to be at the party before Amanda is? If you really don't think you'll be able to stand firm and turn her away, have your mom and/or her mom over a bit early, and if Amanda shows up, your mom or her mom can be the ones to take her aside and turn her away. Heck, her mom can even use the line above. "Oh, Amanda how nice of you to stop by with the kids on your way to dinner. Hope you all have a good night at home!"
Do not bend. Do not cave. If you need your partner and your mom and Amanda's mom to run all the interference, have them do it, but don't let her trample all over your party. This is your party, it's your rules, and you're not doing anyone any kindness by letting it be taken over by Amanda and her kids.
I agree, tackle this head-on.
In fact,
you can say, "Amanda, I hear that you are planning to bring your children to the party even though I've alerted everyone that it's a grownups-only party. And that you are counting on the idea that I won't want to hurt your kids' feelings by turning you all away.
"That would be really, really unfair to me--I sure hope that's not the case.
"But before you promise me you wouldn't try to take advantage of my fondness for your kids, let me point out to you a couple of things:
"Many other friends are either not attending or are paying babysitters in order to enjoy a non-kid night. It's something they're looking forward to--if you bring your kids, you're messing that up for them.
"Also, some of them would have brought their kids if they could--but I told them they couldn't. If you come with your kids, and I let them in, then my other friends will be mad at me, and it would be your fault.
"So, given that I've heard this rumor, I have to say this to you: Unless you can promise me, in this conversation, that you will not bring your children to the party, then I will have to un-invite you."
I love Zizi-K's:
"You know, it sounds like you're going to have to skip the party altogether. This is a bit too much stress for me to handle to go back and forth with you like this, and for my own sanity I'm going to have to rescind the invitation. Hopefully we can catch up next time you're in town, and I hope you and the kids have a good NYE." It's not rude to do so when the guest has made it clear that they intend to take blatant advantage of your hospitality.
Define this for what it is. She is creating stress, she is creating drama, she is making this difficult.
