Unfortunately, the only celiac test that does not require you to be consuming gluten is a genetic test. However, some 30% of the population has the genes that can develop into celiac disease. Only a tiny few actually go on to develop it. Doctors use the gene test to help rule out celiac disease -- not diagnose it.
If you have decided not to do a challenge, then you should probably stick to the GF diet. If you find that you can not adhere to the diet because you have doubts, then consider a gluten challenge for a biopsy. It is only 2 to 4 weeks compared to the blood test which requires 8 to 12 weeks.
Exactly what tests were given for celiac disease? I ask because if it was the TTG, that test, if slightly elevated or in your case borderline, could be due to other autoimmune issues or Lyme disease and not celiac disease. You can see why biopsies are still the gold standard for diagnosing celiac disease.
If your kids are consuming gluten, then ask your doctor to screen them for celiac disease. That might help with your diagnosis.