One, obviously, avoid wheat entirely. I probably don't need to say it, but I've had some family members who tried to just "reduce". It doesn't work.
Two: You may not know things like this exist, because they may not just be on the shelf of your local pharmacies: https://smile.amazon.com/dp/B00CHQAM08 Now, the box is basically a lie, inasmuch as you can't just pop one of these pills and then eat whatever you want. However, if you have reason to think you're going to do something questionable (such as, say, have the part of the family that doesn't really keep the gluten separate, or go out to eat somewhere), I'm about 99% confident this stuff really does work and can help, even if it doesn't "solve" the problem. You can even take it an hour after you eat, once you realize what has happened, and it will still help. Won't solve everything. But it helps. Sometimes the "use by" dates are very conservative on things; for these I've found these do tend to go bad quickly, and they may cause minor digestive distress downstairs, if you know what I mean; still worth it.
Three: In my personal experience, the real problem with celiac isn't "I feel ill when I eat wheat." That is, ultimately, just an inconvenience. The real problem in my life is that I have difficulty absorbing nutrients, even after I've long since stopped eating wheat. My big challenge has been what I'm fairly sure is "paroxysmal atrial fibrillation", which I didn't realize was trashing my sleep for years, to the point where I couldn't even get to sleep anymore without my heart doing all the things (PVCs, skipped beats, hard beats, bleh). The doctors I went to declined to diagnose me, but it worked out because they'd probably have thrown pills at me. I now take fistfuls of vitamins several times a day. It looks rather scary, but for me has been a life changer in a good way, and when I don't do it, I immediately suffer. I would advise reading up about vitamins and minerals and their various symptoms of deficiencies, and considering trying some of them if any of them strike you as relevant to your life. In general, a place like HN will say that supplements should generally not be necessary and you should just eat well, and while I generally agree with that, you specifically have strong Bayesian evidence to consider that you may find certain supplements may help you a lot.
As far as I know, while there are studies that establish the general truth of what I've said above, there are not very many specific studies that discuss which nutrients you are specifically likely to be missing. My personal experience is that I really seem to have trouble with the minerals, though I've also had good experience with taurine (with its friend l-arginine, heart related), vitamin A (didn't help my heart but it gave my immune system a huge kick in a good way), and vitamin K (with its friend D). YMMV. If you specifically have a heart issue, reach out to me (see HN profile) and I can get more detailed; it's a bit long to put on HN. If you don't specifically have that issue, you'll have to explore on your own. Or maybe you have it relatively lightly compared to me; my father has a much less strong version of it and does fine on a small subset of what I have to take. If this is all foreign to you, and you sleep great and have no issues, just ignore me and count your blessings.
Oh... and my #1 food-I-missed was cheesecake. New York style, rich as can be. If my wife says "I can't eat this, it's too rich", it's just the right amount of rich. Fortunately, it doesn't really need wheat. Here's my recipe, which I've been updating over the years: http://jerf.org/Cheesecake.txt