False negatives do happen. It delayed my diagnosis for many years. However if you want to have celiac related testing done you have to be eating gluten. If you have stopped and improved and any introduction makes your symptoms come back then you know that your body doesn't want it. That will make a challenge difficult.
You should get the total IGA and IGG done. I have never seen a 0 for those gliadin related tests before. Doesn't mean it doesn't happen I have just never seen it.
You both have very low B12. A sublingual supplement will help with that. Do ask the ped before giving it to your child though. Low B12 is quite common for folks with celiac.