That is the correct position for towing and it is good that the battery has been replaced.
You should not have a drain in that position so you will have to find what type of draw there is on the system when it is in the OFF position by installing an amp meter between the negative battery cable and the negative battery terminal to see if the drain is less than 50 milliamp.
If one of the computers is staying powered up you may have a 200 - 250 milliamp drain but even that should not completely drain the battery if you drive the car daily or every other day.
If it is left for days or weeks on end with the key in the ignition then the drain may be a problem but with daily driving and a new battery as you have you should be able to go for several days even with the higher drain.
Let me know how fast the battery dies and I might be able to suggest something to check that does not require a meter to be installed for the amp draw test
NO you need to find the drain or see if the battery has a bad cell that is much too fast for a computer staying on so you need to have a drain test run to see what the pull is. If you left the doors open and the interior lights on for three hours the battery would not be drained so this is a major draw and the cause will have to be found.
If you have an amp meter install it between the negative terminal and the cable and see what the draw is with the key in the off position.
I suspect you will see 1.5 - 2.5 amps and pulling fuses will show what circuit the draw drops to normal levels then working down the circuit will show which component is the problem.
If you have auto lights be sure they are in the off position as there can be current flow through a headlight bulb without it glowing, same for the other lamps.
If you need a shop to chase the draw they should be able to find it within 1 hour labor time, I would not take it to a dealer if you do need a shop. Find an independent, certified shop that claims to be an electrical specialist.
You should not have to have the car attached to the RV to find the draw it should be present whenever the key is in the off position or there is a problem with how the wiring to the RV is installed in the car.
Let me know what I can do to help you with this