I soooooooooo now how you feel and I only have one kid!
Ds was a terrible eater, at the start of this year he was eating a yogurt and maybe some organix crisps in a day. That was it.
Now, he is still very fussy (and sometimes "needs" fed unfortunately!) but will eat more fruit and some veg and eats cereal, carbohydrates etc. I thought Id never be tough enough to do the whole 'its that or nothing' thing but it IS the right thing to do. we did do the 'soft version' of it though. So our routine went like this...
8am - breakfast, cereal first then toast (so kind of giving 2 options there but he got the second even if he had eaten the first)
lunchtime - main option (eg sandw) THEN yogurt then offered other things on a 'snack plate' so things like cubes of cheese, banana, dried apricots, ham, crisps, apple etc etc (again got this snack plate regardless of whether ate main bit)
dinner - main bit (usually some kind of pasta tbh) followed by yogurt/ fruit.
supper - anything from crumpets to toast to roll to tomatoes, apple, crackers etc etc
Sorry this is a long post but basically he got other things to eat such as yog or snack plate or supper or whatever even if he DID eat lunch or whatever meal. Therefore he didnt see it as an alternative but it still gave him the opportunity to fill up iyswim? Also, it meant he didnt think he was 'winning'. I never offered him something like a different main meal (eg pizza instead of pasta etc).
Ds still has crappy eating habits in other ways but in terms of actual amounts and variety he has improved. Oh and we cut out snacks until he improved.
Dont worry about teh nutrients thing too much - you could give tonic / supplements??