The parking brake works the same in both directions.
So it should be a transmission issue, not the parking brake. You know you don't have to put it on the parking brake every time, don't you? So try without it.
The parking brake is implemented differently from the main brakes:
https://www.realoem.com/bmw/enUS/sho...diagId=34_1972. Also, there is a maintenance advice to keep it going strong: see the
manual, page 61. Also, it should not be used for prolonged period of time, especially in winter as the pads/shoes can freeze. Actually it only has to be used in addition to the transmission's parking mode (and a slight turn of the wheels towards off the road) on a steep slope.