Firstly if you want her to have veggie juice please make your own as V8 juice is full of salt! PLus it uses vegetable concentrates so they could contain any kind of additive plus the drink would probably have been heated which means its nutrients are no where near as good as fresh!
I would say her behaviour is due to her low blood sugar levels so she would need an afternoon snack - you can put veggies in smoothies! Try an afternoon smoothie with A2 milk, plain yogurt, strawberries, blueberries , ice and a handful of baby spinach leaves , once blended the blueberries keep it a purple colour so no hint of green!
Or would she eat carrot muffins ? Does she like dips? Raw veggies are sometimes easier to eat - capsicum/cucumber/carrot sticks and tzatiki?
I make veggie chips for my fussy nieces, just sweet potato, pumpkin, carrot or beetroot sliced paper thin with a veggie peeler, spray olive oil over and bake for 10 mins until you have chips!