Hi Lucas and Josh's mom,
This is from reading and my childhood experience (my lo is still in diapers), but a couple of things came to mind-
Experts say a child needs to be exposed to a food at least 40 times before he sees it as familiar, so that might help when you think,"We've had asparagus every night this week and they won't touch it." 40 times is a lot. And they say 40 is the average. For some kids it is more.
Also I know from being a picky eater myself, it became all about the power struggle between me and my parents. The good thing they did was not let me snack, so I eventually ate something, but it was usually bland, boring ood and a few bites of what they would make me eat (like veggies). I didn't become a healthy eater until college when I was away from them and it didn't feel like "letting them win" if I tried paella (something a picky eater would die to look at). I know how bad that sounds, but it really bugged me so much to lose face to them that I would not eat certain things. I think it just became too big in our house. I am trying to be really low key about what my ds eats because if he has my stubborness we could go through the same thing. (And my mom will be smirking all the way). This said, I have healthy eating habits now because my parents had modeled healthy eating habits, so even though I was a pasta and butter girl most days, now I seek out crunchy veggies and healthy food. So, hopefully it is encouraging to know that your efforts WILL pay off, but it might take a while. Just don't let it become a power struggle.
Then the only other thing I can think of is trying to trick them with cheese on veggies, let them make some of the food themselves, have lots of healthy dipping sauces in cool cups (kids love that), and totally staying away from snacks FOR SURE.
Something else my mom made me do to prove to me that helthy snacks were best was to make a food pyramid chart to hang on the fridge. We looked it up, she drew the pyramid and wrote out the titles really neat and I drew the foods- what was an art project with mummy at the time became the law of snacks once it found it's home on the frdge. Example, ME: "Mom, I'm hungry." MOM: "Have you had your three servings of veggies today?" ME: "No, there's nothing to eat. " MOM: "Well, look at the pictures and pick something. There shoudl be lots of healthy choices in the fridge." ME: "I don't want to." MOM: "Well, I guess you're not that hungry." ME: "Fine." And even though this seems like it failed, it didn't because if I were hungry I did get a healthy snack and I knew she woudl never let me have something else to fill up on. Eventually the conversation got easier on her side and I ate well.
I hope this isn't too long. Maybe your LOs aren't even THAT picky. But having been a picky eater myself who has good eating habits as an adult, I am sure my mom's strategies had everything to do with it. She is very much of the "start as you mean to go" school and does not give in easily so I always knew what she wanted. Maybe she made it too much of a big deal since I fought her on it off and on throughout my childhood, but here we are today and we had lunch together yesterday: black bean omlette's with live yogurt and fresh parsley. It was yummy.
Sorry this became some long and herky jerky, been writing between moments of being "on duty."
Keep us posted on what works.
Good luck!
Valerie, a recovering bad eater