JWA has two terminals, Terminal A and B. All flights will lead downstairs to where the baggage claim is (either in Terminal A or B). This is the direction out towards the rental car and pick up area anyway, so just follow the crowd.
The car rental kiosks/desks are located next to the baggage claim area, in between the two terminals. Since I'm not a special member of any car rental agency, I always had to check in at the kiosk to sign paperwork/show id first, then went to the actual pick up spot. The actual rental car pick up area is found in the underground level of the parking structure across the street from the terminal (really short walk).
Once you pick up your car, you can get directly on the North 55 freeway (then onto the 5 North) from the airport. No need to hassle with surface streets. Light traffic (avoiding rush hour traffic 3-6pm) to DL will take you about 20-25 minutes.
My suggestion is have your family wait for the baggage come down while you walk check in with Budget (in the terminal). Meet with them, and all go down to the actual car pick up and be on your way. By going solo to the car rental pick up, there is no real easy way to pick up your family unless you loop the airport and come back and park in the offload/pick up zone.
