You need a 2500 minimum for sure. A 3500 SRW would be a better choice considering the size of the family. Kids grow and get heavier, thus so does their luggage. If your state does put a penalty on a 3500 I'd guess it's based on the GVWR being over 10,000 pounds. Look into buying a 3500 with only a 10,000 pound GVWR. We just did this at work. My boss tries to save money anywhere he can so we bought a 2015 Chevy 3500 SRW which normally has an 11,500 GVWR but you can order it like he did with a 10,000 GVWR. It's the same truck, nothing changes except the label on the door.
Don't dismiss buying a new truck. The one we bought was gas, 4wd, 4 door with few options but I think it only cost about $35,000. I think Ram also offers a similar option on the GVWR and the Tradesman package is the one I would pick if buying a new truck. I don't go in for heated door handles, power cup holders, and 37 air bags.