Hello Jay,
Here is the schematic for the 2008 210P if that is indeed what you have. Hopefully you can read this and know schematics, see the Isolator in the drawing. In the isolator are two silicon power diodes the anode of each are connected to the large center stud (terminal A on the drawing) which comes directly from the alternator positive output, with no circuit breaker or fuse.
See pdf drawing file attached......
In your photo, as on this drawing, the left large stud (terminal 1 on the dwg, and "Rig" on yours, goes to the engine battery directly. No circuit breaker or fuse. The power diodes aren't SCR's, and will only connect via the anode --->I--- to the engine battery, but not allow any reverse current if the alternator is not running.
By the same token, the other diode is allowing the alternator to also charge the house batteries as it is connected to the large right stud (terminal 2 on dwg) but in that case there are two 50 Amp auto reset circuit breakers in the line to the house batteries. The voltage drop across these diodes may be 0 .7 Volts
So if you read the alternator voltage when the engine is running you should get around 14.5 Volts or more, on the center stud A, with your negative lead on the negative battery post. If you then move your red lead to the left terminal 1 Rig stud it should also read above 14 Volts with the engine running.
And you should see that voltage at the engine battery positive post as well. If you lose the charging voltage at any of these points then the battery will not be charging.
Here is an interactive demonstrator that will show you the charging paths for alternator, generator or shore power charging on your RV:
Click on the appropriate ON /OFF buttons to see the charging paths for engine alternator, Onan generator or Shore power sources.
If you are losing the charging voltage we'll have to go to the next step. Let's see what you get for readings. Do you have a 120 VAC battery charger with you on this trip, a portable one? If you have ground power or running the genset have it charging your engine battery until this is resolved.
Note that the Tripplite battery charger for the house batteries does not charge the engine battery, which is a serious design flaw in the system, and why Booster suggested a two way relay type isolator. It seems you need to take some voltage readings while you are on this trip. I have to address that on mine, but I'm preparing to change to LIFePo4 house batteries and so charging them with the alternator isn't so simple....
I sent you a message.
Pete