Cooking for my kids
When you say picky eaters what is it that they do like to eat?
Something that might work is having one night a week where they have to try a new food. Be it a vegetable or fruit even something like tuna or chicken salad. How old are your kids? Any of them old enough to help you cook or prepare the food?
I personally would talk with Emma and say something like "hey Emma I would really appreciate it if you help me make better and healthier meals for all of us" and ask her if there is anything that she would like to try making. I know 16 can be a tough age to get them to engage in doing things, but maybe look up healthier meals on Youtube together.
As for the two younger ones again slowly start introducing a new food each week. Not sure if you and your family eat out or do fast foods, but there are so many different hacks out there that can make those McDonald's chicken nuggets a healthy food that is made at home or really any other fast food can be made as a healthy alternative at home.
I always think outside the box. One of my go to snacks is a dill pickle wrapped with cheese and deli ham or chicken. It might seem strange, but its good and filling.