I agree that an already sensitive child should be kept off of dairy, including dairy in things like mashed potatoes, etc. Blood in the stool is an important sign that needs to be noticed and respected.
Two of my children are sensitive/allergic to milk. I've found that they can tolerate cultured milk products, like yogurt or buttermilk, okay. (So I've learned to do a lot of cooking with yogurt and buttermilk--lol)!
Many children who can't handle cow's milk can handle goat's milk, which is very similar in composition to human breast milk, so that might be something to try and can probably be found raw.