Sat,
If it stops when you disconnect the battery, then (as you noted) the battery is not the problem. What is the problem is the alternator or its connections.
You said you ohmed things out. I will assume you have some kind of meter. So, Let's do the whole diagnostic starting at the top.
As said, the battery is not the problem, but it should be 12.6 if fully charged and at 12.0 is about done. If we are in that range lets go on.
Start the main engine. Now, find the post on the back of the alternator. Measure voltage there. There may be a cover that you have to get past. Measure both the post and the cable terminal. They should be the same. (If not, clean the connection.)
=>If it is the same as the battery, the alternator is toast.
=>If it is way higher than the battery, there is a bad connection.
Keep moving down the alternator output cable until you find where the voltage changes some amount. If it is a connection, Fix that. If that does not change things, keep going down the cable.
There are two different means to attach alternators to RV systems.
One is beast called an isolator that is a large heat sink with three (or more) terminals. If you find one of these, again measure voltages. Usually the alternator is in the middle and the house banks is on one end and the main engine start is on the other. If it is working right, the alternator post should be highest voltage and the other two no more than 0.7V less. If it is different than that, you problem is close by. Each of those terminals goes off to a battery.
The other method is called a charging contactor or combiner and it looks like a Ford solenoid. The engine power is on one side and the house is on the other. When the engine is running, both posts should be the same.
There is some strangeness that can happen with these, so if you have not found the problem by now, come back here with what you do find and I will make suggestions for other tests.
Matt
Matt & Mary Colie
A sailor, his bride and their black dogs (one dear dog is waiting for us at the bridge) going to see some dry places that have Geocaches in a coach made the year we married.