If I were you, I'd look for a new/used 10x10 chainlink dog run and use that to make a run. That would be 4 10 foot long, 6 foot high chainlink panels, and you could make them a 10x20 run easily by using the back wooden fence as a side. Basically the same shape that you've got going now, but it should be large enough to enclose the coop inside it, then cover the whole thing with bird netting (or that chicken wire you've already got if it's enough) to keep them inside. Then you've got then fully enclosed and a full gate for you to walk into the run/coop area.