Onyxelle--
I suspect those two adorable, strong-willed children take after their mama.
As far as the field trip goes, you have promised to chaperone and you don't want the teacher scrambling for a chaperone at the last minute--she's be sure to tattle to Santa ON YOU.
Anorexia is not a characteristic of pre-schoolers. All the same, your daughter probably senses you are concerned about your weight and cutting down on portions. If you turn her diet into a battleground, she just may play in the big anorexia league when she hits her teens.
Meanwhile, by rejecting and wasting food, she's learned to push your buttons and play you like the mighty Wurtlizer Organ. Tell her that YOU have decided that food will no longer be a battleground. SHE can control what she will eat, but YOU are the adult and YOU will be sure that she doesn't fill up on junk. You can't make her eat vegetables--but you can deprive her of junk (at least until she's more physically independent). SHE must have some vegetables in order to grow healthy and strong.
Three bites of vegetables (and make them small bites). For canned and frozen vegetables, check the package labels and inform her of vitamin and mineral content. For fresh vegetables check out:
http://www.nal.usda.gov/fnic/cgi-bin/nut_search.pl
This isn't you against her--this is you helping her cooperate with the USDA and the NIA and the Ancient Archives of Maternal Common Sense.
Also, lady, how do you like your vegetables? Only for show? Only with lots of butter? Strong willed toddlers imitate strong willed mothers.
Remember, the idiot that announced that just before Christmas children "are as good as they can be" didn't know much about children.
Good Luck. Have fun with Santa. Hold your dominion.