I had changed the battery to a non-OEM but AGM battery two winters ago. Now I'm paranoid that the change may have caused some of these problems.
Dealership was focused on a bad Transfer Case Control Module and I am not convinced. The TCCM but I don't think the TCCM is involved in trailer tow mode or the different sport modes which the vehicle likes to switch between on its own. I told them if they don't find anything wrong with the switch on the dash, or the harness to it and verify the BCM and TCCM software versions, and a CAN bus ground inspection, I just want the vehicle back.