Please do not trap and relocate. Not only is it illegal in many states, you're probably dumping your problem animal on someone else. You do need to build a better, more secure coop. Enclose the top. Reinforce your cattle panels with hardware cloth. Even if you trap whatever your current predator is, you will have more. As previously stated, everything likes chicken.
You sound a whole lot like me when I was your age. I would build all kinds of things. It's fun isn't it? Good luck to you. I hope you don't have any more losses.
