We use reg. mustard--have never seen a mustard w/ gluten in it. If someone's fussing about the vinegar, I think you're fine.

Oats are controversial...supposedly they can become contaminated, so some buy $$ GF oats from dedicated producers. My personal opinion? That if you are reacting to that and millet? It's the carbs/starches, like you said.
Are you soaking them in an acid medium? We aren't bothered by oats then. Truly, in our house, it's not the gluten, but the starches that go with it, and wondering if that's true for others.
What kind of reaction, BTW?