OK....in simplest terms;
You're stating your tow capacity is 9400 lbs.
Power wise....I'm assuming you've done your research, and that that number is accurate. Honestly, with a 3.42 axle and a 5.3l gasoline engine, I'm finding that a bit hard to swallow. I haven't researched your truck, so I could be wrong.....but a modern Dodge 2500 with a 3.42 axle and a Cummins Diesel is only rated at 9600 lbs. Go to a 3.73 axle, and it jumps up to the neighborhood of 13K. Go to a 4.10, and it's around 14,500 lbs. That's a 3/4 ton truck with a diesel. So power wise, I think you're in over your head even on flat land. In the mountains towing up 8% grades where I live, that trailer will eat your lunch.
Now, even if it is 9400 lbs....you've got a trailer that's scale weighed at roughly 8350 lbs, correct? You are at about 89% of rated capacity before you put a fiver hitch, a drop of fuel, or anything beyond 154 lbs of driver. You said 400 lbs for driver and passenger + 2 kids. Lets call that 550 lbs. You are now at 8900 lbs. Add in 35 gallons of fuel x 8 lbs per gallon. That's another 280 lbs. Throw in a fifth wheel hitch setup....I'm guessing 150 lbs for that. You are now at 9330 lbs.....or 99.25% of your trucks rated capacity.
The closer you get to the limit, the less fun towing will be.....your scenario would terrify me....it would be a white knuckle thrill ride on anything that isn't perfectly flat. I'm towing a trailer that GROSSES 7700 lbs and isn't loaded anywhere near that, with a truck rated at 1200 lbs more towing capacity than you, and I wouldn't want any more trailer than I have.
The closer you get to the limit, the quicker it will wear out your equipment too. Towing on the ragged edge of mfg recommended limits strains EVERYTHING. Your car engine probably has a RPM limit (red line) of about 6000 rpms....can you imagine running it there all the time?
Seriously....we're just trying to give you sound advice here and keep you, above all, SAFE. Your scenario is leaving ZERO margin for error....what happens if you lose your trailer brakes (a blown fuse away from reality) coming down a steep grade? What if someone blows a stop sign in front of you?? Can you stop that monster that's bearing down on your from behind? What if you get a wind sway? Can the truck control the trailer, or will the tail wag the dog?
I know...I'm not telling you what you want to hear, and ultimately it's your decision. Do whatever you think is best.