When we had our HTT (in sig), we first started towing it with our Astro Minivan. We had the Equalizer hitch system and it worked great, but as the van's steering components would get sloop, we'd feel the push and pull of trucks more and more. That's when I knew it was time to replace the idler/pitman arms.
I don't know if it as a problem with the Astro, but it seemed these components would get sloop quickly. After replacing them, the push and pull of large vehicles would disappear. Tired of replacing these components, we switched to using our Nissan Xterra to tow the HTT and problem solved.
Now that we have a 32' Class C Motorhome, we occasionally feel the push and pull of passing large vehicles. Paying attention to the side-view mirrors can really help to anticipate and control the problem. Just moving a few inches away from the truck as it approaches usually does the trick, assuming he doesn't drift towards us. This helped when towing with the Astro too.
-Michael