I am a parent and have a toddler and a preteen, and yes you let your daughter boss you around in this instance. They won't starve to death and you don't need to punish them either. Its their choice to participate with the family in meal times. Its not reasonable that everyone gets exactly what they want when they want it and its wrong to give in to those types of attitudes. Kids can compromise, and its funny how the food becomes magically appetizing an hour later when their stomach is growling.
Yes parenting is hard, they are emotional terrorists, but you are implying you have no choice in the matter. I'm not saying you made a bad decision either, just blaming the kid for it is problematic.