I don't think any of them have - "pick a car drive off" lots for elites. Avis and Hertz don't at least, not sure about Enterprise. I don't have a ton of experience picking up there, but I've seen madhouse times and completely empty times at each of them.

The first thing that came to mind though is that it might be easier for you to park the family somewhere next to the terminal with the luggage, hop on the airtrain and then bring the car back around. Depending on which terminal, folks here can probably suggest a good spot.