Well, I have never done mobile pen, but you could use cattle panels, and if your fence is like that it would work. If you are around more to get them out OK or have them dehorned it helps get rid of the problem. Just have all with or without horns. Goats don't like to get wet so they will need a mobile shelter which I do know about. Your pen must be big enough that they can't jump on the shelter and over the fence. An old timer said get rid of the fence climbers and jumpers or they will teach them all.
I built a shed like this: I bought two 4x4x10's for one and 8' ones for the smaller one (you could use landscaping timbers). I cut one in half and screwed it on each end with big lag type screws. I then built a frame on that 4.5 at the rear and 5.5'at the front. One of mine has privacy fence all around the sides and back for the walls which I Like better than the tin sided one to avoid cuts. Tin roof, I attached four big screw in hooks to the corners so I can pull it across the ground with my truck though putting wheels on it like a tractor coop that can be raised while sitting, and lowered to move from old plastic mowere tires would be better. Then I put a hay rack,a plastic mineral thing with two slots for loose minerals and baking soda, and a plastic grain with a metal divider on the wall feeder like they sell at Tractor Supply.
Lesson learned, the hard way. Don't try new things in a too-small round pen. -Banti
