You need to get transit visa from Saudi Embassy or any authorized agency can help you in that, for you and your whole family. ( along with other documentation of car etc).
Saudi will not give you visa on arrival no matter what profession you have.
Once you are done with Saudi transit visa, other formalities for trip in car, then i suggest you give a call to AMER( UAE Immigration Customer services ) they will guide you on visa on arrival. Except Saudi, rest all GCC countries give visa on arrival to some of the approved professions.