One of my 1st thoughts after reading about the 2x weekly loose stools was a food allergy or ibd/ibs/colitis - but then I see that you home cook. What are feeding? I wonder if she's having a reaction to something. Loose stools twice a week is def. not normal. Has she had a fecal test?
Plus the rash, and her feeling "hot" - it almost sounds like a systemic histamine reaction to something...but what? Have you had her allergy tested - that might help?
Poor baby! I feel so bad for her, she sounds miserable. But, she has a good Mom who is trying to get to the bottom of this. I'm sure others will have good suggestions - so hang in there and have faith that you'll figure this out!