Battery Charging Problem

[Lucky Penny]

I'm having a problem with my Battery charging system and am tearing my hair out trying to figure it out. The problem is when the engine is running the charging system will only charge one battery. With the isolation switch on batt. 1 everything is fine. When I switch to batt 2 the volt meter drops to 12 volts and continues to drop to the point where the engine stalls. I've switched the batteries with the same results. I've also tightened all of the connections I can find.
Thanks for the help