LindsayB, You might want to make a phone call to your local Department of Wildlife or Fish and Game and find out what you can legally do with a trapped Raccoon. Last year I had a problem with one trying to break into my house. It actually almost made it in one day, middle of the day with my wife and two dogs standing not more than a few feet away. I called the Department of Wildlife and found out that although I could trap it without a license or anything like that. Once I had it their was nothing I could do with it except kill it right where it was. It was illegal to transport it as well as release it. IT was actually illegal to even open the cage and let it out again, not that anyone woudl be able to know if I did that. Basically I just woudl not want you to be out turning coons loose and run into trouble you didn't even know you could get into.
As for your run. I agree that it is cute, but anything but safe. I have a run that is both. My first thought when I saw your run was that you have some great decoration and it is actually a nice start that can be added to. If it where me I woudl go get 4 8 foot long 4X4 posts and plant one at each corner of your run. then put 2X4 across the top of these. you can then cover this frame with hardware cloth and have a very secure run. you can still have the picket fence running around this for the visual effects it gives. This would give you a wire cage that is 6 to 7 feet tall. As for the coop, keep in mind that coon learn how to open latches of all kinds. securing against them can be a real challenge. They are also strong so be certain that boards and other parts of the cop cannot be pulled off. One thing is certain, if you stop them one one way, they will simply look for the next weak spot.
Best of luck, coons are a tough predator to beat. I know they are my primary concern here. I simply built so strong they don't have a prayer.