Trucks and trailers can be parked ONLY in truck parkings or house parkings, not in car parkings.
When you are in truck with trailer, type /park and truck and trailer both will get parked.
After that if you type /detach and then you can move your truck freely somewhere else and park it somewhere else if you want, while trailer will stay there (where you had parked).
If you have Auto park, then if you detach your trailer in a parking, then it will get parked automatically, if you have disabled auto-parking from /preferences then you have to type /park for parking (manual parking)
When you are in truck with trailer, type /park and truck and trailer both will get parked.
After that if you type /detach and then you can move your truck freely somewhere else and park it somewhere else if you want, while trailer will stay there (where you had parked).
If you have Auto park, then if you detach your trailer in a parking, then it will get parked automatically, if you have disabled auto-parking from /preferences then you have to type /park for parking (manual parking)