You probably find it a little disrespectful because IT IS!
If her kid came over to your house and said "I can't eat chocolate because it gives me a migraine", would you say "You'll eat what I give you!" and hand her a chocolate bar? Of course not.
Wheat causes her physical pain - trust me, I've had the ER give me morphine for heartburn once, and I've had 2 large babies with no drugs, so I'm no wimp. Has your daughter explained that to her?
At age 10, it's tough because you're still learning to be a human all on your own and not an extension of your parents. It's tough to stand up for yourself when a (supposedly) grownup tells you you're being stupid, but it's a good lesson to learn.
I would gave a talk with the other mom, explain that this isn't a healthy child trying to lose weight or anything, it's a food sensitivity. Then try sending your daughter with some Lara bars or good beef jerky or some other food that doesn't need refrigeration. Have her just pass on the foods that have wheat, and tell her to call you if this other mom gives her flack about it so you can pick her up.
Alternatively, have her daughter come to your home instead.
I definitely think focusing on the "food intolerance" side of it will get you a lot further.
But she may just be an obnoxious, controlling person, in which case you will have to decide if you want that in your life.