Always replace both batteries
It doesn't matter if it's a flashlight or an RV, if it has two or more, replace them all.
As for your question about replacing the Tripplite, that's outside my knowledge but the Forum has lots of threads on the subject; check them out. The gist is, replace the Tripplite with the newer, more capable Magnum. It's quite possible the Tripplite's high float voltage fried your batteries.
All the best, Dave the Scourge of the ION