If your mom is a type 1, she is probably used to injecting the correct amount of insulin to cover her carbs. That's why she could serve up burgers and potato salad with chocolate cake and still eat. You don't say how old she is, or how tightly she controls her own blood sugar levels, but if she is casual about it, she may think that Amanda doesn't need kid glove treatment. She probably doesn't truly understand that Amanda doesn't have the same 'freedom' that she enjoys.
It sounds to me that Amanda made the best of a difficult situation- my hat's off to her. It sounds like you are doing a great job of educating her and she is accepting the responsibility to take care of herself when mom and dad aren't there. Next time she wants to spend time with Grandma- trust her to take care of herself, send her with supplies she can fall back on when grandma brings out the goodies, and make sure she has a cell phone so she can call you if she needs an ally. Teach her to say, "No thanks, I'm not hungry right now" Rather than, " I can't eat that" - Choosing not to eat a food that is not in your best interest is far more empowering than being denied.
Once she gets more settled into her new situation- maybe you could help her test out some foods like chips that she really wants to be able to eat so she can feel like a normal kid, or at least not paint a bullseye on her back for the other kids to aim at. You might send her with a dish that she likes- I'm sure grandma would be willing to warm it up!
I went through this with my own kids- we are vegetarians - and kids that eat yogurt and tofu are bully bait. One of my daughters traveled extensively with musical organizations- she learned early how to request the foods she needed and to reject the foods she would not eat with grace. Both remain vegetarians - my music daughter is married- and her M-I-L recently told me that other relatives were surprised to find out that Kristen doesn't eat meat- she never makes demands at family get togethers, and always finds enough food to eat from what's available. She always brings a dish or two that she can eat ( and makes her husband save her some because those dishes go fast), and has a protein bar in the car to snack on if need be.
BTW: If you ever figure out your mother- please let us know- I'm still scratching my head over what makes mine tick- lol
AMM, then, it's your mom's problem. And my guess is that she sees the light switch but won't turn on the light. It really is shocking that she served that food, so it's all about control as you wrote. Amanda is still your daughter and you'll continue to make sure she eats what she should. It's wonderful that she is cooperative and doesn't fight what she needs to do. You're doing the right thing, seriously.