Here's my take. Your truck with airbags (assuming 18" or 20" wheels and 6500 lb RAWR) is every bit as capable as a SRW 3500 of the same year. Literally the only difference is the rear coils, but the rear coils with supplemental airbags should carry a load at least as well as the 3500 leaf suspension. Everything else between the two trucks is identical. Well, except you have a rear swaybar on the 2500, which I don't think the 3500 has standard - so that's actually an advantage for your truck.
That being said, based on the trailer weight numbers posted, I think this trailer is pushing into DRW territory, at least if you plant to load it up to the full GWWR. I've said before and I still believe that on these newer HD trucks the difference between a 2500 and SRW 3500 is a whole lot less significant than the difference between a SRW 3500 and a DRW 3500.
There is a difference in the posted capacities of the 2500 and 3500. We know he has a 2014 Ram with a 6.7 cummins. I assumed everything else to show the difference. Lets say it is a 4x2, crewcab, automatic transmission (DG7), 3.42 rear, and tradesman trim.
According to the 2014 Ram Body Builder guide:
2500 in this configuration has a payload of 2,660. Rear GAWR of 6,000 and GCWR of 25,000
The same configuration on a 3500 SRW has a payload of 4,190. Rear GAWR 7,000 and GCWR of 25,000
They have the same GCWR, but the payload and rear axle limits are considerably different.
The trip sounds wonderful and I hope you and your family have a great time.