You are absolutely doing the right thing, stick at it
Oh how I remember this battle well & I feel for you as it is stressful as hell until you recognise it for what it is - it's their little control game, mine took it to the n'th degree in that it was not only what she would eat, but how many spoonfuls - everything was treat like poison, even though it was often her favourite foods & she demanded to know how many spoonfuls she had to eat before she could leave the table - she would then try & barter me down on how many 
I had a classic with mine - we went on holiday & I promised myself that for 2 weeks I would not allow myself to be dragged into this game as I was on holiday & needed a break from the stress of it
Day one in the self service restaurant, she starts demanding to know what she could choose to eat, when I made suggestions, she refused everyone & so it began - after a few minutes I said, "you know what, I'm on holiday, I'm on strike, so I don't care what you eat, eat any rubbish you like, or don't eat at all, your choice.
The look on her face was a picture - she then stood up on her chair & threw a tantrum, screaming that I was a rubbish mum because I didn't care if she ate properly, playing to an audience who were now looking at her, she went on to tell them all that I would just let her eat junk food for the rest of her life & die young, so I was a rubbish mother & didn't deserve kids - she was good at drama
- DH & I were trying hard not to laugh & I knew then I had cracked it - is tucked to my guns & just shrugged "but you keep telling me you are a big girl now"
Day one she deliberately piled her plate with nothing but chips
By the end of day 2 she was choosing the things she actually likes best, which was fish, salad & vegetables & we never looked back.
I would recommend a book called "Vegetable Glue" it's just a kids story book, but aimed at them understanding they need to eat veg & it went down well with mine.
She's now 12 & eats an exceptionally healthy diet, breakfast this morning was a bowl of strawberries, banana & pecan nuts - her choice
She does occasionally slip back to my needing to cajole her with some things, but it's clearly an attention seeking comfort thing when she's feeling down or unwell, she's owned up to that
Good luck & it will pass 