Towing Travel Trailers

You didn't say what you tow with or what hitch you have. I tow a 37ft. travel trailer 10k gvwr with my GMC 2500HD and have an Equal-I-zer brand integrated sway control hitch rated at 14K/1400 tongue wt. and do so just fine with no issues. Your statement about "sway bar" is telling that you may not quite understand hitches yet. The Equal-I-zer is a weight distributing hitch with built in sway control by means of friction on the weight distrubiting bars and 'L' brackets they rest in. The other is a friction antisway device added onto the side of the tongue and connecting to the hitch head. I have used this type on smaller lighter trailers but would not use it on a 35 ft. trailer because it is inadequate for the weight it would need to suppress in a sway situation. Look on youtube for how to handle sway should you experience it.