A 7000 pound dry TT will be every bit of 8000 pounds loaded for a long weekend with 1000 pounds of tongue weight. You likely have about 1450 pounds of payload to support your family, things to occupy their travel time, and trailer tongue weight. Your Yukon will be over the tow rating, GVWR, and rear axle rating. You also have a 1000 pound tongue weight receiver limit.
An F-150 with 9100 pound tow rating may also be over some of its ratings too. Since this is a RE, I'll assume you have do not have children to bring with you. Stick closer to 6k dry and I think you'll be much happier. How about the Keystone Passport 3180?