I totally agree with your last paragraph. That sums it up for me too! Well said.What is that white sheet material the dogs tore off the coop sides? Is that metal or plastic/vinyl? It looks like plastic to me the way it is broken apart. I think the only way to keep large dogs out of a coop or run is to build it very heavy, everyone recommends using hardware cloth on this forum and it is the best stuff you can get for keeping out normal small wild predators but it is not strong enough to deter a strong predator nor is that sheet siding. I would recommend using something like chain link fencing or heavy welded wire dog kennel sections, the heavy guage welded wire is probably going to be stronger than chain link though chain link will work as well as it is not a super determined dog with a lot of time to work at it. Then put your layers of hardware cloth or chicken wire over the top of the heavier fencing to prevent smaller animals from getting in. Also I am building a shed style coop which can contain all the birds over night or during bad weather or times when there may be danger around, no dog or anything else will get in this coop and it will be locked at night. An electric fencer with a strand or 2 down low may be beneficial too if you continue to have these issues.
Hog panels are another option of very strong fencing, this is probably the route I would go if I didn't have any extra dog kennel sections available.
I personally don't believe it is the responsibility of a livestock owner to have to spend a bunch of money to build super strong enclosures to deal with dogs who shouldn't be there in the first place, you should be able to free range your animals on your own property if you so choose without worrying about roving dogs killing them, I refuse to build an Alcatraz chicken coop and run and have to keep them enclosed at all times to prevent some jerk's dog from attacking, I will kill the dogs whenever they come around, I have a duty to protect my animals and family the same as they jerk dog owner has the duty to keep his dogs contained. Losing a few birds to wild animals is annoying enough but domestic animals like dogs and cats killing them really puts me over the edge.