When it comes time to take the fat/oil off, fold a piece of paper towel in half and lay it flat on the soup, uhh, glue. The towel will absorb the fat in preference to the water/glue/soup. Your wife probably knows this. Really, making glue is the same as making a good broth just use hide shavings and sinew in place of oxtails.
Another way to get the fat off is to pour the liquid into a tall, narrow bottle. The fat will concentrate in the neck. Suck it off with a turkey baster.