Wow that must be very frustrating for you! Since I'm not the mother of a diabetic (actually I'm not a mother at all unless your counting taking care of my animals lol) I can't really relate. But, being a teenager, I suppose I still have an opinion about everything :)
My parents never kept me from eating because my blood sugar was high. Occasionally I choose not too because when my blood sugar is that high, I'm just not hungry, but food is always an option. I guess my parents thought it was unhealthy to skip a meal or something like that. I really don't know their reasons...
I suggest Chloe carry an extra site change, as well as a spare syringe or two. That's what I do. When my blood sugar gets to be over 300, I'll use the site change and instead of correcting by pump, I do it by shot. It tends to work a bit faster than the pump. Also, I'll disconnect from the pump and tell it to give my correction, so then later when I re-check, I can look at my pump and see how much IOB I have. It helps keep me from taking too much insulin and crashing.
Try talking to your family and telling them that if Chloe's blood sugar goes above or below a set number, that you MUST be called. My parents did that when I was younger. When I got my own cell phone, it became my responsibility to call them when my blood sugar goes crazy. When it does become her responsibility to let you know, just know that occasionally she'll either get lazy or forget. I do it all the time. Hey, we're just kids. We're not perfect :)
Hope I helped in some way, shape, or form!