I have a "standard" Reese weight distributing hitch (WDH) with one anti-sway bar for our 21 foot trailer. If your trailer seems to be swaying back and forth while simply driving down the road (no wind pushing it, few bumps, etc) you should look at a few things. You shouldn't NEED a anti-sway bar just for normal driving down the road - the bars simply help reduce sway if it occurs.
Short answer - Yes, adding a second sway bar will help reduce sway. But...
Is your WDH actually setup correctly? I towed my rig for a few years setup with how the dealer put it on. Towed okay, but not great. I found that by changing the angle slightly on the hitch coming off the truck and changing how much tension the weight distributing bars had, towing improved greatly. Check the website for your hitch manufacturer for info on setting up the hitch, also read all the how-to articles scattered about these forums.
Also, how is the weight distributed in your camper / TT ? Many times sway can be reduced by moving some weight to the front of the TT, but don't over do it! Preferably, you can go to a commercial truck scale to weigh your rig all hooked up and see how much weight is on the hitch. I found that by just moving bed sheets / sleeping bags to the front of the TT while towing, the towing seemed to be better.
Hopefully some of this helps!