NQC - Think Sunday's were like that because my dad was home. To be fair, he was only strict because of the fact he grew up after the war when you had to appreciate whatever food you were given. Anyway, weekdays it was eat or nothing. So out of a dinner such as liver, bacon, beans and mash I would eat the bacon and mash. Or for a stew, I'd eat the meat and carrots nothing else.
If we ate dinner than we'd get a pudding so my sister and I would take it in turns to go upstairs with food stuffed in our apron pockets and flush it down the loo. Our parents would think we'd eaten it, then we'd get dessert.
The best two food weeks of my childhood came when I had my tonsills out and I was allowed to eat ice-cream and jelly and mushy stuff, til dad caught me eating a Penguin bar and the gig was up!!
I am now a very fussy eater. I dont think it was caused by my parents desire for me to eat the same food as them / healthy food, I probably would have been as much as or just more a fussy eater if I'd been able to eat whatever I liked. My reasoning for this being that my younger sister was spoilt slighty, she was such a grouchy baby that she could eat whatever she wanted because it was the only time mum and dad got any peace. She's just as much a fussy eater as I am.
However, Pagan, at two I dont think it is going to do your child any harm as she is so young. Try it for a while and see how it goes, you wont be losing anything.