I think it's important to determine here what it is you want most of all.
Is your number one, above all else, no matter what priority that the child not be in your house at all? Even if that means your friend doesn't come to your party at all? If so, then you're on the right course. But if you will be upset if she can't come to your party at all, then you may want to rethink. You can't take a hardline stance about the kid and then harbor any complaints if she respects them - but stays home.
There's really nothing *wrong* with either stance. Neither are rude, and neither are patently inappropriate in friendships. You just have to decide where your feelings are.
I know that I've been in analogous circumstances before where I thought one thing was The Most Important Thing to me, but then I realized that if people respected that thing, and in so doing, declined my event, I'd actually be upset. And that meant I had to rethink how accommodating I wanted to be. I had to ask myself 'just how important is it that this person come?'