Ok, here what I did today,
With the RV generator working, I check the voltage of each 12v fuses at the bed, on each side of the fuses. They all read 13.65 v.
Without the RV generator, or plug to the shore, only on the coach batteries, I check the voltage of each 12v fuses at the bed, on each side of the fuses again, they all read 12.16v.
This is the same voltage I have at the batteries.
With the RV generator working, I check the voltage at the BCC on both pole of the selenoid for the coach, both pole had 12.10v.
Here the catch, the charger positive wire goes directly to the fuses box, the BCC coach wire pole goes (I assume) directly to the fuse box also. They are side by side on the fuses circuit board. The charger in order to charge the batteries need to be able to see the voltage of the batteries, since it's a 3 stage charger and stop charging at 13.60. The charger, at the fuse box see 13.65v, so no need to charge.
Now, looks like I have to investigate why I'm able to read 13,65v at the fuse box and not something like 12.6v.
I don't know what is that circuit board. Just a fuses sockets board or more complicated than that with diodes and others components!
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