unlikely, cos uretha is above vagina and anus is below it.
so they are separated by quite a bit.
Sometimes though when you pee it dribbles and sprays everywhere and probable seems to be coming from butt
I think she just has severe diarrhea. Taking a diarrhea medicine and getting lots of fluids should fix the problem. Unless she has a stomach virus or food poisoning. Is she throwing up as well?
If she's on a fat blocker like Alli, it could cause leakage of an oily discharge that could be mistaken for urine. Eating any 'diet' foods cooked in olean or olestra can cause the same problem.