I thought maybe doing a trial period to see if he reacts positively to being gluten free and then adding it back to see if symptoms come back would maybe be helpful to the doctor? But I guess that's true, it might skew things regarding any future tests that might be warranted.
If you haven't had her tested yet please do not go gluten free. Get the celiac testing first as if she does feel better gluten free when she has to go back on gluten for testing she may have much worse symptoms. There will also be a higher risk of false negatives.
I did not mean to imply that you should put him on a gluten free diet. If you suspect a problem with gluten, please get an opinion from a GI who is celiac savvy. All celiac testing requires a patient to be consuming gluten.
The slightly equivocal TTG? That warrants a gene test at the very least.