A couple of terms I don't understand. When you talk about a trickle charger, is this the converter(inverter/charger that keeps batteries charged and provides 12v power for house systems? Also, a transfer switch changes 120 v power from shore cord to generator.
The voltages you report are much too low for charging. A 12 v battery is fully charged at 12.7 v, it takes about 13.4 v to overcome internal resistance and start charging, most charging goes at ~14.4 v to charge.(absorption charge) As the battery comes up to about +95% charge, the charger will go to a float charging mode, providing about 13.4 v to finish the charging to 100%.
You need to clean and inspect all connections, including ground connections. Also check and see if your converter/charger has a temperature probe on the batteries. If that is unhooked or broken it will cause the charger not to work properly.
having to replace 3 batteries in a 2 year old RV points to charging issues. If you can't figure it out, it would be worth it to have it checked out to be sure you don't kill more batteries!