Does the coach have a box of many buttons, video slector or something of this nature to select inputs to the various TVs? If so I would first verify cable service on the primary TV (just to be sure, again) then swap the coax feeding the primary with the external TV at the video slector box. Rescan both for cable channels. If the external TV still won't find cable channels but the primary does then the problem is probably the TV. If the primary doesn't find channels but the external does the problem is the switch box. Since you can scan for over the air channels the coax to the exterior TV is OK. The other option is to run a temporary coax from the cable TV feed (external to the coach) directly to the TV and see what happens.