My 3 year old son is in a picky stage and it's causing some grief between the hubs and I. He's a "You have to eat what's on your plate or face the consequences" type and/or he'll make him sit there for what seems like hours, which my son doesn't mind doing, but I hate seeing him sitting there a long time. I don't like making a "thing" of eating.
I've never allowed any wrong behavior at the table, rudeness or demanding of "other food", but if the kids don't want it, they sit nicely until everyone is done and don't eat again until the next meal. Since my husband travels constantly, they are used to my way. Neither style has "made them eat" things they don't like. To me, not liking food isn't bad behavior, so I let it go.
If I were you, I would not make her sit there and battle, but I would not feed her anything different and she could wait until the next meal. She will not skip meals for 7 days straight or anything (or even one or two). Just feed her things she likes with no veggies at separate times. But make sure she is HUNGRY when you offer her the veggies, and she's more likely to eat them if she knows there will be no option. Meanwhile, she's not going to deplete her health. I know kids who never eat veggies because their parents don't even try. I think mother nature takes care of them to an extent when they're young and going through this.
If my husband were you, he'd make her sit there all night before giving up. :-0