I can't see how it would be the coach coax wiring or connections if the Antenna signal works well on all the TVs... if you have a BOMB(Coax/HDMI switch box) generally the coax from the outside connection comes into it, then out to all the TVs - the same with the Antenna signal.
Is the box pressed for 'CABLE' for each of the TVs?
with the switch box, it probably doesn't matter if the 'ON' button is pressed, as Cable doesn't require it, but it probably would not interfere with the Cable signal even if it is.
'14 Thor Palazzo 33.3 compact diesel 100k+miles since '14... US, Alaska, Canada...
AND a '14 Gulfstream Amerlite
AND a '07 ForestRIver Rockwood