Your Dad is probably right -- but then us old dads usually are. ;D
Your Jayco probably has a Gross Vehicle Weight Rating (GVWR) of around 6500/7500 lbs. Your receiver probably has a Class IV, 5000-lb weight bearing limit. You should be using a weight distributing Class IV or V hitch system for your trailer which would raise that limit over 10K. A weight bearing hitch setup loads almost all the traiiler tongue weight of the trailer (around 12/15% of the trailer weight) onto the rear truck axle moving the truck toward an unstable oversteer condition. A WD hitch moves a portion of that weight onto the front axle restoring the normal understeer. This is a worthwhile improvement in ease of driving and in emergency handling. Adding a sway control to the WD hitch provides an additional margin with crosswinds and emergency handling.
We like to recommend a WD hitch system with integral sway control. Two reliable such systems are the Equalizer and the Reese/Staitline Dual Cam
units.