This is an issue between you and DH, frankly.
Actually, now that I think about it, I believe that its solely DH's issue.
He sounds like a classic "pleaser." In your home, he goes along with you and your preferences in terms of diets, allergens, etc and tells you what you want to hear. I would be willing to bet that at your ILs home, when they roll their eyes at your issues he goes along with their doubt and tells THEM what they want to hear, and lets your kids eat what your ILs want them to eat.
He is just trying to keep the peace and keep everybody happy and avoid confrontation. So that leaves you thinking that the two of you are on the same page, and I would bet that your ILs think he agrees with them that your food issues are just made up.
If I were in your shoes, I would push this issue with DH hard. What does he truly believe in his heart of hearts? Does he believe you that these food issues are real, or does he agree with your parents that you are overreacting and this is just a fad? Then I would INSIST that his actions line up with what he says he believes. And I would call him on it EVERY SINGLE TIME he doesn't "walk the talk."
If DH believes his parents are correct and food intolerances are not an issue in your family, then he needs to own that and have it out with you.
If DH believes that you are correct in how you are handling your kids' food, then he needs to have your back with his family every single time.
In short, he needs to seriously man up.
I don't think you should force an apology from your FIL, and I don't think you should waste your time trying to convince the ILs of the validity of your choices. They don't get a vote in how you feed your family. If you try to get them "on board" and convince them, you are inviting them to argue back. Don't waste your time. You and DH should decide what is best, then case closed.