Actually, it probably "IS" the battery charger and/or isolator circuitry causing you the problem. Running a separate power feed to the radio most likely will not solve it.
RV and trailer makers are not known for using topnotch components in their standard models. You have a couple of choices. First, you could replace the charger with a more robust one and hope that it is better filtered. However, the selling price has little to do with how much and how well the unit performs in the real world.
Assuming a multi-battery setup, if the charger runs through an isolator (most single ended ones do), the isolator may be causing some of the noise, if not all. After all, they are diodes, they get leaky, etc.
It's a big pain, but I'd go looking for the source with a potable AM radio. If you have a VHF radio with an AM mode, that's better yet. Obviously, knowing the source is 90% of the battle.