Food is one of only a few things they can control, so it really doesn't seem like a good idea to make it into a battleground. We won't win.
I follow the idea of it is my job to offer healthy food and her job to decide what and how much to eat. Some days this is very frustrating as she will want to just eat bread and cheese but other times she eats a lot more balanced. DD just turned 3.
DD doesn't eat meat (will not touch it, never has), so there is often something we are eating that she won't. I don't force it. I always offer her a taste of new foods but respect her right to say no. Last week she said yes to fish and liked it. I've offered it tons of times before but last week she said yes.
I don't usually make her a completely different meal, I just make sure there are foods on the table that she will eat. I try to avoid processed foods. I make bread so if she wants bread and butter for a snack I know it's whole wheat and not full of additives, at least. If we make pizza or pasta, it's whole wheat and I sneak extra veggies into the sauce. If we have pancakes, they are whole wheat and have apples, pumpkin or bananas in there. Oatmeal is whole oats with apples shredded in there.
I think a lot of kids have texture issues, sometimes it is a case where intervention is required. For the usual kid though, just model eating a variety of foods, offer (without pressure) tastes of yours. Talk about healthy foods outside of mealtimes. Avoid bargaining "you can have a cookie if you eat a carrot." That sends more of a message that carrots are icky. If you get a treat for eating them they must be bad.
Dr. Sears has a nutrition book that might help. Sneaky Chef and Deceptively Delicious might give you some ideas of adapting foods she will eat to get more goodness in them.
My DD won't eat sauce on pasta but she will dip bread or cheese into the sauce and eat the pasta plain, so consider alternatives. I know a lot of kids like dips (not mine).
Also kids often will eat stuff they help prepare. Get a kid cookbook from the library and get her involved. That may expand her eating. Consider new foods outside your comfort area too. I am sometimes surprised at the ethnic foods DD will want to try and then like (she eats sushi, for ex but won't touch more normal foods).
Good luck, I know the food thing can be so frustrating. Try to let it go. If it is a case where she will only eat 2 foods or something like that, talk with her doc to see if something else is going on. But kids this age are picky, some much worse than others!