Battery shows 3/4 on shore power. Full on charger?

If your looking at the lights on the main panel in your MH, then that is your problem. As for checking the battery the only sure was is a load test. Take them out, fully charge them on your battery charger then take then to a battery store and have them load tested. Finally get yourself a volt meter and learn how to use it. It is invaluable for diagnosing electrical problems. Cheap ones worn as good as expensive ones for home use.