Tamara... I totally agree with everything you have said.
My 4yo was a good eater at childcare, but at home has always been limited in what he eats, but as he eats, meat, Apples, Bananas, grapes, various grains/cereals, Mash potato (with puree veg mixed in) & dairy, I'm not to worried as in a day he eats from each food group... My 2yo is much the same, although eats more veg .... I was much the same at 2-5yo stage & my brother ate everything, now as an adult, he is VERY fussy & I eat pretty much everything (except Lamb, cos it gives me stomach cramps).
The best advice I got as far as food is concerned "A child will NEVER starve themselves & it is the parents responsibility to offer healthy food & a child's to choose how much & when they eat it" I can tell you a 2yo can live off air & water for 2 days... cos mine does quite often, he just looses interest in food & then a few days later he eats more so much food it is unbelievable.
As Tamara said 2yo love to have control & if you give them something to let them have a power struggle with you over, they will take it & run with it... where as at childcare they children realise that no one cares enough to have that struggle.