Just a note: the place where the chickens sleep and nest is called the house. The fenced playground area is the run. And together they are called the coop.
I see you are rather close to your neighbors. This brings up two thoughts.
ONE: Have you checked to make sure your coop is far enough away from the property line to meet any building codes in your area? I know someone who had to completely tear down and rebuild a hen house with cement floor and fence posts cemented in the ground because she didn't check with her local building codes first. (Just trying to save you some heartache and additional costs here.)
TWO: Have you thought about putting some privacy fencing on the side that faces your neighbor's property? This might help prevent some stress your birds may face if there happens to be unruly children, dogs, cats in the neighborhood. My nearest neighbor is a mile away, so it isn't an issue for me. But I have noticed that most hens squawk very loudly when they are disturbed. And once one of them starts squawking, they all join in. The disturbance could be the lawn tractor or the rototiller or geese flying overhead. The loud squawking may not be appreciated by your neighbors, so I think a privacy-type fence would block some of the things that might disturb the birds. A free dozen of eggs will help smooth any ruffled neighbors but won't solve all your problems.
As you probably found when you were working with it, chicken wire is very flimsy and flexible. A determined predator can and will push against the chicken wire and fence posts. Since the wire is flexible, it will bend against the predator's weight. As a precaution, I would put up a second fence with smaller holes and made of stronger material; hardware cloth or ag wire fencing are good. Are your fence posts cemented in the ground? This will help make the entire fence stronger.
You don't say the dimensions of the house. Standard sized birds do best with 4' per bird and bantams can have less space. I have standards and am not sure of the bantam numbers. For the 30 standard sized birds you said you want to have, the house should be 120 sq feet (10 x 12). It is better to build it to the size you want to have, unless you plan to build a new house or an addition to the original for additional flock members. Remember birds that have more space while confined indoors have less health issues, less pecking and less possible cannibalism.
The 25 x 25 run includes the house, so is really a smaller area than that. I don't have a fenced run. But one of my friends used to have a run like yours that ended up a complete mud area. So she moved her chickens to another part of her property. In her new chicken area, she first dug up the sod, put down a base of pea gravel and then covered the gravel with the sod to help with drainage issues. The rain and snow drained better and the grass didn't get as muddy in the new area. She also plants grass in wood boxes and lays it like sod over any areas in the run that do get damaged. Her new area is almost 2 years old and still looks pretty good.
Shade in the run is a good idea. You can put a tarp across the top of some of the run. You can use a piece of plywood on sawhorses, or an old table. You could even use some old beach umbrellas. A covered area will also give your birds a place to hide from flying predators.
The thing I have found about predators is that once they see or hear or smell that you have chickens, they WILL find you, as you have found with those dogs. Get down on the ground and look at your coop from their level. Push on the fence, check for spots that can be dug into and under. The only way to keep a digging predator out is to dig a trench and lay heavy duty hardware cloth or sheet metal about 6" deep. Good luck with the mothballs! (They didn't work for us. :| )
Will you just have the large door for the chickens to enter and exit or will you be installing a pop door for them?
Remember that the cayenne pepper and chilli pepper will need reapplied every time it rains.
Locking the flock up at night is a good thing. You'll sleep better for it, if nothing else.
I think you are off to a good start. Don't forget to post pics when you've got it done and your birds!
regards,
keljonma
if edited, probably for typos...