Like with everything else, for your daughter's happiness and security, she needs to know you are in charge. You mention her psychology-you don't want her to feel confused or like she may be in charge if she wants to be. This causes terrible twos and unhappy whining and tantrums etc. leading to parental disrespect and bigger problems later if she thinks you're a wimp.
Whatever YOU decide for the food program in your house, You must enforce. If you have a lifestyle which is busy and on the go, family meals aren't important to you, and you feel she should eat whenever/wherever she wants, then make that the system, and don't worry about it. Don't expect her sit nicely at a table and eat down the road-because that won't be what she has learned, but just go with the flow and do it. Don't "lose a battle".
If you want her to eat her food at the table whenever you serve it, then that is what you must teach. Every child will fight it (and everything else) as human nature at first. It's not about the task at hand, it's about control. My extended family (very large families) makes children eat meals at the table, and eat what they are served, so from the time they can sit up, they are served in their seat at meal time and no bad manners are allowed. They are treated and included like they are already part of the group and must behave accordingly. If they refuse to eat, they just get water, and no snack, until the next meal. Any disciplinary action needed for playing with food etc is handled in itself, but the actual "eating" isn't forced.
For new "yucky" stuff, like veggies they haven't had, they only have to (and it's enforced) eat a few tiny bites before moving on the the part they like. Gradually they get used to them and eat normal servings. Within a few meals, they learn that there isn't an alternative to what/when they eat and good table manners are never in question.
This system totally worked for me, my 2 and 1/2 year old eats well at the table and in restaurants and gets to have snacks in between. but at first she didn't get snacks, because I was having a hard time getting her to eat meals.
Don't worry, your daughter will not starve. Eating is the oldest challenge in the book for kids-the ultimate power play. Pick a lifestyle and enforce it. Your strength and love as a mommy is the best gift you can give her.
GOOD LUCK