I,m not qualified to tell what you should do, but it seems to me you have answered some of your own questions.
Pin worms 3 times in the last 3 years? Consider a parasite cleanse.
"they both react to milk (and somewhat to sugar) with sassy, mean behavior. It seems to make them very angry"
Cut back on the dairy and sugar. Particularly the Baskin Robbins. Have you ever read the ingredients in some of the commercial Ice Cream? Besides loads of sugar, there is also loads of other crap with 15 letter names that you can't pronounce.
If you have read this forum much you had to come away with the fact that Sugar is bad and that a healthy Diet is the answer to good health. Your children are at a perfect age that you can adjust their diet so that they can be healthy now as well as later when you're not around.
Children learn from their parents, the good as well as the bad.