I agree with your wife. And for the trailer you describe a DRW is not needed. My 5'r weighs in at 14,250 and my F350 PSD pulls it just great.
Not only is the dually width an issue. But so is the 8 foot bed length. Add a crew cab and that is one long (and wide) truck. Especially when turning in tight spots.
Those that have dually's rationalize their capability. And if it works for them....great. It's not for me. And not needed, either.
A F350 or 3500 in later model years will handle the task just fine. If you are thinking more along the lines of 16,000 pounds, then you need a dually.