Veggies - have you ever tried "frozen"... as in, not thawed, not cooked - still frozen? Both my kids went through a phase where the only veggies they would eat were french fries... and frozen veggies: frozen corn/peas/carrots... Frozen veggies don't taste like veggies... they just taste frozen! (as teenagers, they still like veggies that way for a snack!)
Sugar high - relates to three things: how much sugar, what else you ate at the time, and what you were doing before you ate it. Protein, fat and fiber dramatically slow down sugar absorption... example: granola bars are high in sugar, but also have fat and sometimes protein, but not enough: add a beef jerky stick, and it makes a big difference. Pop is horrid... unless they've been working hard in the yard all day - at which point their blood sugar is actually depleted, and the impact is reduced.
Breakfast - dump the boxed cereals. Seriously. Old fashioned cooked cereals have way more food value. Sweeten with brown sugar or maple sugar or honey for fantastic taste. Our kids eat it daily, even when we travel. Add an egg to that, or some sausage. THEN they can have bread and jam, and there's no sugar impact! Besides, cooked cereals are CHEAP!! (and no, you don't need to even dirty a pot - but that's another story)
Just some ideas...