M.F.
I was having a battle with my son over dinner every night. Everything that I made he said he didn't like, even some of his favorites. I came up with the idea that he could choose what was for dinner one night a week (within reason - no ice cream for dinner or anything like that). Once a month we let him choose that we can go to any restaurant for dinner on his night if he would like, but you might not want to do that since your daughter eats out a lot with her Dad. On the nights where I choose what is for dinner, if he doesn't like it then he can eat carrots with dressing and grapes. I let him choose the carrots and grapes, but the rule was he had to choose a fruit and a vegetable. For the first few weeks, I made sure I always had carrots and grapes in the house. The first few days of the plan went well, then we had something that he didn't like (although he had eaten it many times before, he was just testing the plan) so I said fine, you don't have to eat it and I got him carrots and grapes and he ate them. Ever since then, we haven't had much of a problem at all. I think he felt that things were being forced upon him and once I gave him a say in the process on a consistent basis he felt much better. There are nights that he doesn't eat so well, but overall he does pretty well and it helps to look at the big picture, not just one particular meal.
I wouldn't worry too much about her just eating a few different types of fruit. Just have the other types available, stick them on the table without saying anything and I bet one day she will surprise you and try some. Don't make a big deal out of it (you don't want her to think that you are "winning" the power struggle), just note to yourself that it is another fruit to add to the list and serve it again.
Also, I like Jennifer's suggestion of having her cook the meal. Since your daughter is a little older, perhaps you can update my plan to say she can choose and can cook what is for dinner one night a week. Remember to make it positive, not negative, that she gets to cook.