Thanks to all who responded to my original post of 1/25.
Yesterday, I met with my technician. He tested the entire system from the battery in the motorhome to the battery in the Honda CRV, including fuses. All tested 100% ok. Voltages were 13+. He inspected the entire charge line for damage/problems; again all ok. We could find nothing either installed incorrectly or working incorrectly that would cause the Honda battery to go dead.
None the less when towing between LA and Albuquerque at the end of day 2 (Albuquerque) the Honda batters is completely dead.
I have had 2 different technicians try to solve my problem but the bottom line is the charge line I have should keep the Honda battery charged while towing.
I am totally frustrated. Help!!! I welcome any further ideas.