Maybe a bit weird but had you tried a different lunch box?
We bought a PlanetBox for my son and he eats much better. I guess it's the little amounts and choice he gets.
Main compartment
Sandwiches/wraps/pitta with Ham/cheese/tuna or leftover meat and a dip or a chicken drumstick with avocado, cold pasta with veggies & sauce, ham and cheese roll ups, chicken and apples, crackers, cheese, ham, salami, eggs, just tuna mayo sweetcorn and a folk.
Fruit compartment: whatever is in season, mandarin, grapes, berries, sometimes I'll just put strawberries and a pot of cream in (he loves this)
Veggie compartment: cucumber, capsicum, carrots, sugar snap peas
Snack compartment: banana, homemade veggie muffin, ham/eggs (depending on what's in main part) home-popped popcorn.
And a small treat compartment which only holds one square of dark Chocolate or a small piece of flapjack.
My son is a fussy eater (getting better) but there's something about seeing his lunchbox open with lots of choice and nicely presented which means he eats more and is willing to at least try any new things I sneak in there.
I agree that pudding isn't needed every night. Fruit fine, jelly and ice cream on Sundays. Even yogurt can be full of sugar if you buy the wrong ones.
Ours aren't allowed nuts, or yoghurt in kindy so will have those at breakfast or afternoon snack. Natural yoghurt with a drizzle of honey, sliced almonds and a banana or berries and breakfast is sorted.
We've also started making smoothies to get more fruit and veg in. You could get a special flask for your dd to take one to school. My dc's favourites are Spinach, Mango and Pineapple or Carrots, apple, peach & Mango as well as the easy spinach and mixed berries.