Oh, You have my sympathy.
my DS (now 27 months) is a little bugger for not eating.. my DD (Now 13 months) is a pure delight!!!
FWIW (and I'm certainly no expert) I never withold milk (both have follow on milk at bedtime and, honestly, DD never finishes hers as she is so good at drinking water and eating so DS has the end of hers too
) but its part of their bedtime routine, so I never miss it out.
BUT... I never offer more than one choice of meal (they eat 3 meals and 2 snacks per day) and it's that or nothing. the only other thing they are allowed to eat is food from my plate (weirdly, they now both love prawn stirfry!!)
They are both allowed one bottle of milk in the morning too. DS has his, usually, around 5am and then goes back to sleep.. DD more often than not, doesn't bother and prefers fruit and porridge for breakfast.
She is sitll little and (I'm guessing) sees the baby having a bottle too... my DS was only 13 months when DD came along and def. reverted to some baby-ish habits (not wanting a cup, wanting a bottle etc) but now that DD is older, they are progressing together.
HTH