Driving from SD, when we get to LAX, should we drop off the rental van first then a shuttle will take us to airport? Or should I drop off my passengers at the airport, drive the van to your office then a shuttle will take me to airport?

Return your rental and then take the rental shuttle to your terminal.

Make sure the petrol is full, the car is clean, then you can drop off your rent car here. The best way to airport is taking the free shuttle, the station is just the near the place where you drop the car.

First give your car away, then there are airtrains to the terminals and you can easy go with your family to the terminal