Rent another motorhome. Seriously. You want to leave in 3 weeks for a 2500 mile trip with a proposed TV that will be over its ratings with no experience towing. Is this a vacation of torque test? That does not leave much time for practice, shakedown trips, or WDH adjustment.
Mid-size SUVs are very limited when it comes to towing high walled RVs with a family onboard. People tend to add about 1000 pounds of items (food, cooking, cloths, towels, spare parts, tools, chairs, toys, etc) for a long weekend. For a long distance trip, you may be approaching 1500 pounds over dry weight. Also, you can expect loaded TW to be in the 12-14% of loaded overall weight in order to help it remain stable. So if you are looking at 6k pounds dry, then, you will likely be around 7500 pounds with 900-1000 pounds of loaded TW. In order to keep all the vehicle ratings (towing, GVWR, axles) under specifications while towing with a family of 4-5, you will want something with at least 1500 (1700-1800 better) pounds of as equipped payload noted on the Tire and Loading sticker, 900+ pound receiver rating, as well as enough tow rating. If you are restricted to FCA, then you're in a 3/4 ton crew cab pickup.
You do not need an integrated brake controller. The better aftermarket ones are under $150CAN and take 10 minutes to install, 9 of which are mounting. Fine tuning the weight distributing hitch is key to comfort and stability. My design is a a little more picky about being adjusted more precisely than most. I have had 60mph feel scary to my wife as a passenger, or 75mph be rock solid with only WDH adjustment differences.