Hay Capt., come over to my house with your trailer and we can run a controlled test of your Omnidirectional antenna and my Batwing. I think that either your batwing is one of the old dipole with out a pc board in the head or there is some other problem with yours.
To the OP, in my never to be humble opinion, if you want good TV reception in your RV, install a Winegar Batwing. It is easy to do if, you want to learn and have the time. Look for a Youtube video on the installation of a batwing. Other than that, camping only where there are full hookups is you only choice and even that isn't always great.