Those so called "omnidirectional" antennas are pretty crappy. Ours completely died a while back so I replaced it with a Winegard Razar Z1 and now I get 26 channels and the towers are between 60 and 70 miles away.
By hooking the antenna to the cable port of the RV you have to have the power supply turned off for it to pass signal. Therefore, the amplifier in the antenna wasn't getting any power. That's why you couldn't get any channels with it hooked to the cable port.
For that to work you'd have to remove the wall plate/power supply and switch the cable and antenna coaxes. Then the power supply would send power out the cable coax and power the antenna amplifier.
I took the old Omni apart when I removed it from the roof and here's what it looks like inside. Notice the nice rusty metal on the disc. It's that way on both sides.