Milk is traditionally considered a good laxative. Mare's milk especially b/c of the higher lactose content. It could be an adjustment period, but it could also be that the amount of lactose she's getting from that amount of milk is a little much for her system. Good news is that cultured & fermented milk causes the lactose to be converted to lactic acid and means it's much more digestible as well as a great source for healthful enzymes and gut-enhancing bacteria. Look up real buttermilk, kefir, or clabbered milk (all starting with raw, of course) as options to replace some of the raw, sweet milk she's drinking.
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The bloody diarrhea does worry me, though, if it is truly the diarrhea that's bloody and not just the wiping. Definitely get her checked out if it is a significant amount and doesn't seem to be from any visible fissure on her anus. E. coli, while present and persistent in our daily lives, can cause bright red, bloody diarrhea if your body has not built up significant immunity to it (hence why farmers' families can usually drink unpasteurized, grain-fed raw milk and we don't get sick from small amounts of it that live in our mouths). Err on the side of caution when consuming raw dairy that isn't from your animals.