AoT Car Service is only available at SBIA/BKK. It is not available at DMK.
Pre-arranging a car from DMK into the City is advisable as the taxi queues can be quite lengthy.
I wouldn't expect to get a van (the largest metered taxi vehicles here are Fortuners, and Innovas) at the official taxi stand.
You could try Grab on arrival, but even then you might get a pick-up, or a Yaaris.