[rdlamb]

River:
Your search for a battery drain villain is excellent. My thought is you may need to check the charging system as well. Hooked up to shore power, or connected to your towing vehicle, you should show the batteries receiving a charge.
You could also put a battery charger on your system and fully charge both batteries, to see how fast they drain after being fully charged.
Finally, what make, brand, and type are the batteries? Is the battery water level full? Low water will greatly decrease the charge.
What are the batteries specs?
The fact that the batteries are new means little, as they could have sat on a shelf for years prior to being used.
Good luck.