It sounds like your BMW is rated close to what my old VW 2.0 TDI Sportwagen was.
It towed well, but the 200 lb tongue weight limit was hard to get.
I never had a stability problem with my 16' (Heavy)
Scamp, but the setup did need the airbags I installed.
I think that you said you had them installed.
I installed a compressor in the side pocket of my VW so I could level the car.
While the VW was adequate and got good mileage and had plenty of power the Town and Country I replaced it with after the recall is better and carries all of the extra stuff better.
I always thought that an equalizer would have helped.
The Canadian RV America (I think) could give you some guidance on hitches.
The VW has a trailer module that makes the car electronics modify the operation for towing and also provide electronic stability control if needed. The module had to be ordered from the UK as it is not available in the US.
The BMW may have the same type of module, I don't know about that.