Well, at least they showed up before you built it, instead of after you built it. I just assume anything that lives in this state will eventually show up looking for a chicken dinner and build accordingly.
I prefer stationary housing for the main flock, but that's because we have severe winters and the rest of the time we free range. If you have to keep them confined, mobile housing to have them on fresh grass is really nice. We built a chicken tractor for a grow out pen and it works great.
You can design your tractor so that the chickens have an enclosed house, with a door that locks, if you want to give them more night time security.
You could also add hinged hardware cloth panels as an apron around the outside edges, to prevent digging. When you need to move it, just flip them up and tie or clip them, to keep them out of the way. After the tractor is moved, put them down again. You can use little landscape fabric pins just to tack down the edge in a place or two, if they need it in some locations. Some pins are made with a nice finger loop at the top, to make pulling them out easy.
I would definitely go with 1/2" hardware cloth on it.