Since the problem went with you from house to house, did you move within the same town? What industries operate in that town.
Do you have house pets? Do you have house plants? Do you have any hobbies that could be problematic? Does anyone smoke? What is your occupation or your husbands?(many people bring home fine usts which become imbedded in their clothing and shed within their home environment)
As far as building materials go, ask about mdf board which is bathed in formaldahyde and is brutal on anyone's health. Carpet is also brutal for many reasons.
The sooner you can play detective and identify the main issue/s the quicker you can take them from the accute reactant phase to the healing phase.
From a dietary standpoint, have you considered trying an elimination diet, then find non reactant foods and place your kids on a rotation diet? This can have many benefits. Is there a environmental doctor in your area? Not to be confused with a traditional allergist.