If you're talking about a "rear receiver hitch" to install on the travel trailer, I don't know of any RV frame that's designed to support that kind of load. So, it's more a matter of "bending the RV frame rails with that much weight than it is "can I tow a 1000 pound tongue load" on the back of my trailer.
Your Cougar 29BHS frame rails probably can't support anywhere close to a 1,000 pound tongue load. If you elect to use a weight distribution hitch, remember that you're going to be adding weight to the Cougar axles, so those "barely adequate tires" are likely going to be even less adequate" with the "WD hitch" placing more weight on them. With a 1000 pound "second trailer tongue weight" you'll also need brakes on the second trailer, so you'll also be placing additional "electric loads" on your tow vehicle brake controller.
If I were you, I'd find a competent engineer to review what you're wanting to do and design a system that won't "self destruct" when towing at highway speeds and you hit an unexpected bump on a public highway.
My guess is that you'll be "way, way over the design limits of your Cougar 29BHS.
2015 F250 6.7l 4x4
2014 Cougar X Lite 27RKS