To make her lunch the healthiest you can, in light of her fussiness, make sandwiches wholewheat with the best quality ham you can afford (watch out for salt). If she is hungry, give her two rounds of sandwiches. The veggie sticks are good, maybe add some hummus for extra protein.
If you want to give her a treat, give her only one and make it healthy, ideally homemade as you can control the fat/sugar/salt and it is cheaper too. Also try sneaking fruit and veggies into dessert e.g. Banana muffins, blueberry muffins, beetroot brownies, carrot cake etc.
Assuming the juice is pure fruit juice and not a juice drink, this is ok. I was brought up on fruit juice being one of your five a day, but the current thinking seems to be that it is not that healthy as it is full of sugar and has no fibre. However seeing as your dd refuses all fruit, currently this is probably a good thing for your daughter to drink.
Also I think you should up her milk intake at home, have a glass of milk with her breakfast or afternoon snack. If she doesn't eat any yoghurt or cheese, (or tofu or leafy greens) she may not be getting enough calcium.
In terms of her general diet, try and do homemade as much as possible e.g. homemade pizza not frozen, homemade fish goujons instead of fish fingers, and when you make pasta sauce and spag bol, stick a load of veggies in there and blend it up.