I've towed tandem for almost 15 years now, but my experience has always been with a 5er as the 1st trailer.
My 1st 5er was a Dutchman, and I can tell you with confidence that it was NOT adequate for putting a second trailer behind it. I suffered through for two years before I decided to upgrade to the RV I have now.
Everyone else has done a great job of covering the tongue weight. What I will tell you is that if you are getting trailer sway, that is putting a TON of stress on the frame of your trailer. Make sure you pay close attention to the attachment of both the receiver hitch on the back of your TT as well as the connection point of the axles to your trailer frame. Both are potentially weak points where excessive trailer sway with a 2nd trailer could cause a catastrophic failure.
Towing tandem isn't for everyone. If you are going to do it, go the extra mile and make sure that everything is set up correctly. When that happens, you should have very little if any trailer sway.
As far as another option, if you are happy with the Yukon you could consider driving a second vehicle to tow the ATV. Almost all cars are capable of towing up to 2000 pounds. Your ATV and trailer should be under that.
Good luck with everything.