Doves can fit through a 2 inch by 4 in hole, hawks can't.
Are you feeding scratch on the ground or in a feeder? You really don't want to feed much scratch in the summertime unless you live in a really cool environment (it can make them overheat). If you are feeding them on the ground, cut back to feeding them what they can clean up in a few minutes.
If the doves learn that there isn't any food in the coop, they will quit going in. The second thing you could do is to put up a bird feeder a little way away from the chicken pen/coop. We have one about 20 yards away from the chicken pen, and even if they do have leftover food, there hasn't been a dove (or any other sort of bird) out with them. Doves only eat food on the ground, so you'll either have to sprinkle some on the ground under the feeder, or let the other wild birds (who will greatly appreciate the food) knock some down. The doves will eventually figure out that the birdfeeder has better food than the chicken pen!
Hope this helps,
Emily