You can purchase a "drip rail" at the hardware store and install it above the hinge area, drip ridge down, usual cost is about $7 and the length is 8' made of aluminum. Are you sure the rain is dripping down or is it being blow upto the hinge area by the wind?
) the other dog is going to take more convincing .... He doesn't believe anything but the occasional beef bit should be raw. I figure even just feeding half and half is better than nothing. 