I checked the water pump tonight. It appears to be working fine. The battery was practically dead before I plugged it in to shore power. The 1 1/2 hour drive back from the coast apparently didn't charge the battery much at all.
Once the battery is fully charged, I'm going to unplug it from shore power and see how well the battery does with sitting for a couple of days. I'll then run the pump, furnace, lights a bit and check the battery again. I might get the battery checked out also. I'm suspicious that there might be an issue somewhere. If not, I guess I'll just have to be a lot more frugal with my power use when I don't have full hookups.