I am glad you see less squabbling. That is great.
You ask if the GFCF diet is necessary. What I am about to say is my opinion, but it is backed up by a lot of medical studies that substantiate my opinion.
I'll give you links if you want them.
I believe it is absolutely necessary. For us, it is more important than removing the other stuff(you shouldn't be giving your sons soy anyway, and you could always buy Vance's Darifree, which we love. My son does not drink it like a kid drinks a glass of milk. We don't use it to drink, we use it to cook with, and in rare ocassions, on cereal, which he no longer likes to eat for breakfast, since I give him such rockin' breakfasts now. This diet is a lifestyle change and can be difficult. but I challenge you to try it for 30 days. 100 percent GFCF, and tell me you don't see a difference. The difference you see might make it completely worthwhile to stay on the diet.
The differences in my son and one of my daughters when on /off the diet are like night and day. MY son is rainman when on gluten, and my daughter is combative, paranoid, and insomniac when on it, plus they bother have physical signs. MY middle child tested higher than all of them and she has very few, if any symptoms.
Google "Gluten intolerance" and you may see issues/ behaviors in your family that can be described by gluten intolerance. What is your family heritage? If it is Northern European (Irish, Scottish, Welsh, English), you can suspect gluten intolerance, although many other groups can have it.
We all got tested for it and we found we have celiac genes, as well as active gluten intolerance. A lot of people do and don't know it. It is very common.
Here is one of a bajillion links out there:
My daughters and I can spot it a mile away, even in strangers walking around. One daughter is a camp counselor and has a running list of kids she believes should be on it!
Please email me with any questions.