Accepting I've never been a parent, but I have some past experience as a child. Seems to me that you create a rod for you own back when you take the easy way out. You need to correct being too willing to cave in, in the past; which I suspect isn't that easy.
And of course it is true that we all have genuine likes and dislikes so one doesn't want to force things on your child they truly do not like, but since they eat the same things elsewhere then we know it is just a power game, she is playing up.
I suspect if she is hungry then she will be less picky. Resist offering an alternative. If she isn't eating then assume she isn't hungry, and take it away until she does want it. Save treats for appropriate times.
The only other thing I can think of, off the top of my head, is that sometimes food textures can be unpleasant. Probably not the issue here, but if it becomes so, liquidising, or at least chopping very small, and adding to something more palatable may allow vitamins/nutrients to be consumed without problem.