One solution might be a
Hensley Arrow hitch. Aside from the anti-sway benefits, the hitch assembly is longer than the standard WD hitch and will allow you to open your truck tailgate when hitched. I have plenty of clearance to open the barn doors on the Suburban while still hitched.
Riverside RV at one time actually built a
TT with an optional kennel from the factory, although I don't think they still offer it.
Two main issues with pets in the trailer: climate control and movement. If you plan to tow in the summer, the TT can get very hot if closed up, so air movement is a must, and even running the a/c from a generator underway is needed in hot climates in the south during summer. The other issue is that passengers in a TT cannot see traffic or what the driver is doing. Regular stopping and turning can be dangerous if someone is up and about in a TT, so a good kennel in a designated area and
permanently mounted to the floor of the TT would be a must.
If I did want to carry pets in the TT while towing, I would want a customized and dedicated kennel area in the front part of the TT ahead of the axles sinec that is where the ride is smoothest. Anything behind the axles gets a lot of bounce, even if you have shocks installed on the TT.
Since most TTs are front bedroom, making proper accommodations for pets is just not practical. Horse trailers are designed with windows that can be fully opened and secured to the side of the trailer for towing, allowing a lot of ventilation, and the horse stalls are somewhat confining so the horses don't move around a lot, and can't be caught off balance if the driver has to brake suddenly. Horses can stand comfortable for long periods, not so much for dogs.
All in all, I would look at either a different hitch or some kind of a different configuration that will enable you carry the dogs in the truck. In the end it's cheaper and safer than trying to make safe accommodations for them in the TT.
You could also look at removing the truck bed and replacing with a
custom kennel setup that will allow the dog s to exit the side of the truck.