First of all, the battery disconnect relay in motorhomes does not have a fuse associated with it. This should be logical because the relay is designed to switch a hot circuit which could be carrying two or three times that much current.
If you are measuring 13 to 15 VDC across your Coach battery terminals then the Converter is trying to charge the battery (15-VDC)or it is fully charged (13-VDC).
From your symptoms, I would have to suspect that your COACH battery is not good. So, how old is the battery? How much water is in the battery?
The battery itself is the culprit more often than other items in RV 12-VDC circuits.