I had wondered why, if Joran had his friends pick him up...and he was with them, and they had the car, why he called Daddy to get him and they just did not take him home in their car. Your thoughts make sense. But, why did the police take Joran's car to inspect? They did that early on, I believe.
Along your thoughts, however, the phone call to Croes, the DJ makes sense...hoping he has some way of disposing of the body off the boat. Maybe Daddy called Lorenzo first, who knew Croes and that is how Lorenzo figures into this. Remember Lorenzo was called in for questioning. He was only there a short time, and released. Next we heard Croes went in (he gave himself up for questioning), and he has been kept.
The first car they took was Deepak's (rumored to be Joran's) Joran does not own a car. Deepak own the silver Honda. Daddy & Mother VDS car's were took just last week. Now does it make sense?