And leave it at that. No expectations. No "she likes me!" if she comes, and no "it is the end of the world!" if she doesn't.
This is why I strongly suggest you, J, don't go to her party or invite her to yours. I don't know that you are in a place emotionally to not try to read into her hand bumping into yours as you serve cake. Or her smiling when you put your hand in the small of her back to get past her in the kitchen. I genuinely believe you aren't ready to put a happy face and fake until you make it twice in a day. Or at all right now. If you were further down the road here I would think maybe this would be a good time to show off how cool, collected and unbothered you are. I just don't know if you have that game face yet. And even if you do I don't' know that you'd make it through the whole day without a meltdown of your own.
And Steve has a point on the nap thing. If you can ensure a good nap for the little you could probably pull off two parties in one day, but if it isn't a must don't force that on yourself or the little one.