Many celiacs (intolerant to gluten) are also lactose intolerant. You
mentioned that she was milk allergic. check out http://www.celiac.com   I
checked this out for my son, and after 9 months of different eliminations
(barley for long time, then wheat, then oats, back on oats, then corn
(which seemed to work), add back wheat. Now 3 months on wheat, he's
complaining of stomach aches again usually at bedtimes, sometimes in the am
signaling hunger or a bm soon. As for the middle of the night, that is very
typical to have intestine pains 3 + hours after eating, after the food
moves out of the stomach.  My daughter, when she was nursing, would react
at midnight to corn I ate at lunch then nursed her in the evenings.