OK, I'm the health nut on the other side of the fence, and even I see she's being out of line. It's NOT your responsibility to cater everyone's diet to this girl's restrictions.
When my daughter goes somewhere briefly -gym daycare, friends houses, etc -and people inevitably bust out the marshmallow spread, and hydrogenated oil, corn syrup (peanut) butter, and god knows what else, I always have a quick, "Oh, thanks so much, we just ate", or if I'm leaving her somewhere, I'm like "Please feed her this." And I have her snacks with me. If they're the stubborn types that will insist she needs artificial cookies and flourescent popsicles, I lie and say she has allergies so they HAVE to stick to what's in the bag.
I also don't freak out if she eats a little junk somewhere, and I let her have a few bites of birthday cake at parties before I mysteriously lose most of it in the trash. But I KNOW most of the world thinks this is annoying, and I don't want my daughter to seem snobby, so I'm building the best habits I can for her and preparing to let her eat badly socially once in a while-as we all do.
What should you do? Ask the mom to send her food in a handy little grocery bag! It's totally easy to do, and I would happily do that if I was leaving my daughter somewhere.
Of COURSE she should at least make you a list, but that's still leaving the burden on you to figure it out and shop for her kid. It should be a simple list of what she CAN eat and the cash to go along with it.
My daughter could very easily sustain herself for 24 hours on some healthy sandwiches-real cheese, natural almond butter, healthy bread, bananas, apples, eggs or cereal for breakfast, organic milk if she still drinks milk. Normal juice without additives. Natural chips. Done. There's a list. All of our major grocery stores have natural alternatives to crazy colored kids snacks and drinks.
Ask her mom if she is allowed to have the cake. Whatever she says, goes.
And if her mom says she can eat anything-feed her anything or let her go hungry! Treat her like any other kid having a fit-don't indulge it. Say that's what you're eating and her mom said it was OK.
Good luck!!!!