As for getting a child to eat right, who buys the food? Who puts the food in front of the child? I never heard of a child starving himself to death if not given what he demands.
Don't make it a contest of wills. Put the food in front of them at appropriate times, if not eaten in an appropriate time then put it away. Give it to the dog if you don't want to save it for the next meal. Above all, do not yell, coerce, beg, etc; this is breakfast/lunch/dinner, the child will eat sooner or later.