My feeling is that motion detector lights will not work - foxes are sneaky, crafty and smart. They will figure them out fast. Better to seal up the coop as best you can. I've never caught fox in a live trap, but I have caught raccoons, possum, and a weasel. Be aware that if you have the trap set and you let your chickens out, you will probably catch a chicken!
My coop is also on the wood line, which makes it easy for most predators, but if I moved it in to the open, I would worry about hawks more. For multiple reasons, I love to let my chickens free-range, but I'm sick of losing chickens. I don't know what the answer is : ( The next thing I'd like to try is to place the coop in a paddock with a llama, alpaca or donkey. I hear they can be protective.