I don't want my daughter to have the issues I have with food, so I never force her to eat. I remember sitting at the dining room table for 2/3 hours trying to choke down (cold and unliked) food so I could leave the table I promised myself I would never do this to my own kids.
If my daughter refuses food offered at meal times, I take it away with no alternative.
However we have certain things she can eat anytime if she is hungry between meals i.e. Raisons, fruit, bread sticks, rice cakes etc. If she gets hungry between meals or misses a meal, I offer these things until the next meal.
Life is too short, to create issue about food.