Seriously, the tea is nasty. I drank some before giving it to her, and had nothing but sympathy - even with her tantrum. I would have done the same thing, especially if I were 3!! I wish there was a better way to treat this... I know, I know, change her diet permanently...
We're getting there.
Considering there's a family history of celiac, I'd try taking her off gluten before making her drink a ton of nasty tea. Probably easier, too. Or do both! I'm trying to think of anything you could use to make the tea taste better, but without knowing what it tastes like, I don't think I can help you. Mom always used to put honey in our herbal tea (Celestial Seasonings herbal tea - gross, with honey - even grosser). Could you mix it with another tea, like a really good chai? I don't know. Sorry. Good luck.