Try having the air temp set blowing at the driver not split between the driver/passenger and floor.
Also take it out of the dual setting and select driver only, NO passengers, this is suppose to make it even on both sides.
Select the coldest temp which on both of my trucks is 60* F, select re-circulate, if you allow outside air in this brings in warmer air mixing with the cold air.
It makes a big difference on mine, especially in 120*, and I never select AUTO.
With it being cold remote starting then warm after you put the key in, something is set wrong or defective.
The first thing I would do is to forget about the dual pass/driver setting, select driver, and select vents only no floor and vents.
Other than these suggestions I made,
next would be the dealer or a shop that specializes in ac.