You know instead of hardware cloth or screening, you could cover the roof of the run so that it keeps rain from going into the run. Tin siding or something like that would work well and help to keep your girls nice and dry. Plus there's very few critters who have the raw power to tear into tin...
I would still worry about something like raccoon's figuring out that weak spot in that coops armor. Maybe you should have used some chicken wire along with the screening? That way they can only rip thru the screening so far. I know you would want to go with something easier to work with than...