It sounds like your DS is pretty high risk for coeliac then, OP. Do you know which blood tests the paediatrician is getting done? Make sure the paed knows the family history, and check that the test includes coeliac screen and which one (there are different types of test).
It might be worth you looking at the Coeliac UK website. They have a lot of info about diagnosis. About 10% of coeliacs are deficient in the antibody (I think it's an antibody) that's used in one of the tests, so check out the info about that to make sure the right tests are being done. Also consider asking for an HLA-typing blood test (which looks for the "coeliac genes" HLA-DQ2 and HLA-DQ8).
Also, at your DS's age, the immune system is not fully developed and so a blood test can be negative but the child can still have coeliac disease. My second son began showing symptoms like his elder brother at about 2.5 - we were very quick off the mark getting him tested, but the blood test was negative. We went for a biopsy anyway, which was inconclusive. The consultant thinks he is coeliac, but we caught it so early that there wasn't enough damage for diagnosis. We have decided to treat him as coeliac, go strictly gluten-free (easy since we're doing it for DS1 anyway) and do a gluten-challenge and retest when he's older.
Finally - since your DS rejects a lot of gluten-containing food, there is a danger that he is not ingesting enough for the test to work. (Although from the way you describe him, it sounds as if he is getting enough to do the damage - if it is coeliac that is the issue.) You should discuss this with the paediatrician as well. In your shoes I would go for the test as soon as possible regardless - and then if it's negative, try and find ways to increase gluten in his diet (even if it is by sprinkling gluten powder into a something he will eat) and re-test in two months.
The good news is that if he is coeliac, the gluten-free diet is miraculous and he will begin improving immediately. Really important to get a diagnosis though - because (as you probably know from your dad) if you are coeliac it is essential that you do the diet properly, avoiding all cross-contamination and being very strict. It is very rare for people to live up to that standard if they haven't had the diagnosis.
The other good news is that I have found that diagnosis at a very young age like your DS's is great for the child's acceptance of the condition. It seems to be much harder for older children/teenagers/adults - I have met people with all sorts of emotional issues around the change in diet. My DC have none of these issues (so far at least) because it's just been normal to them from the start.
Sorry, very long post!