Hmmm...I don't know if I would trust the people that wouldn't let your daughter bring food or asked, "How important is it that your daughter doesn't eat meat for just one day?" It might not be exactly the same thing, but what if your daughter was diabetic or hypoglycemic and you asked if it were ok for her to bring sugar-free treats/extra snacks or if she had a food allergy?
Tell them what mouse said. That should work. Most people wouldn't mind if you put it like that. The parents of your daughter's friend probably know she's a vegetarian and are expecting something like that anyway or are wondering what to feed her.
As for those moms online, I would explain to them your reasoning. They might not know what is veg*n and what isn't. They might feed your daughter something with chicken broth, lard, gelatin, etc without realize it isn't veg*n. (That and all of the junk food they might be feeding her.) Tell them that you're trying to save them some work.
If all else fails, you could always feed her before she goes over and when she comes home the next morning, have breakfast or brunch ready for her. Have her bring some snacks to share with everybody (or just herself if they're being that anal about it).
Totalmuggle--my suggestion is to bring your own meal with you when you go to Grandma's. She's obviously not willing to make something for you (I don't blame her--cooking for that many people is more than enough work), so I'd bring a couple of things that are vegan with enough to share (if nobody wants to try them, you'll always have leftovers and that's a good thing). I'd bring a starchy dish (like a rice stuffing, pasta salad, or vegan mashed potatoes), a meat analogue or a bean dish, and maybe some dessert. Have her set aside some veggies and you can cook them without butter when you get there--bring some vegan margarine with you and have her use it in place of butter if you need to.