I don't have any advice to offer the OP, but I do want to offer encouragement. I used to be a very fussy eater when young, but I now enjoy my food greatly, love to cook and am a massive foodie.
As a young child I would only eat meat and starches. I would be suspicious of fish, would refuse to eat any fruit except bananas, and no green vegetables. I also disliked dairy products and would not drink milk, eat eggs (in natural form), cheese or similar stuff (as I also had a massive sweet tooth, things like custard or flavoured yoghurts were OK).
I can well remember the viscerial feeling of disgust when confronted with such suspicious articles as tomatos or cooked carrots, and my body used to scream at me not to put this frightful thing in my mouth. I remember one occasion when my mother cooked a dish with a baked cheese topping, and I actually ran upstairs and vomited, simply because of the smell.
My family used to tease me considerably for my fussiness. I knew that I ought to eat better, but I resented the comments because I really really didn't want to eat those things. It wasn't a rational reaction at all, and so no amount of teasing ever made me consider trying new things. I remember my primary class doing a project on healthy eating, and the teacher saying seriously that "there is someone in this class who should be very concerned about his diet". I froze, thinking it must have been me (with hindsight, I realise there were probably another couple of boys who ate worse).
As for how my DM handled it; she was an excellent cook who cooked from scratch most evenings, and so things like chicken nuggets and chips were never on offer. I am grateful for that, becuase I think if I'd had them too often I would have latched onto them like crack cocaine. As it was, I now realise she was very patient indeed, offering me what I would eat, always putting veg on the plate, but I don't remember her ever insisting that I ate it.
At school I ran around, playing plenty of football, cricket and British Bulldog, and don't recall having any ill-health.
I would say that it started to wear off in my teens. My family have always enjoyed their food, and that meant there was always a positive feeling about food. Mum was always interested to know whether we liked the dinner, and when she cooked something new, would always ask whether it should go on the 'again list'. We always ate together, and were a happy family, so there were always plenty of reasons to 'opt-in' if you see what I mean. By my mid to late teens I was making vegitable soups and things like that, and when I moved away from home, I found myself cooking all manner of different things quite naturally. Apart from cheese, which remains firmly off-limits, there is just about nothing that I won't eat.
I do not know if I have particularly taste, but I do have a keen sense of smell, and apparently the two are related, and I was interested to note the comments above in the thread on this point.
So I just want to encourage the OP that all is not lost - if you all enjoy food as a family, and set boundaries without allowing the angst to get too much, there is every reason to believe things will come right, as it did for me, an ex-fussy eater.