What is the toe in reading? Too little toe will make the coach wander just as you describe. Too little caster will reduce the coaches tendency to straighten out when turned, resulting in wandering. Too much play in the steering box will result in sloppiness when steering on dead center. Too tight of a steering box results in the steering sticking when making small corrections on center which makes the coach wander in the lane.
The easiest thing to change is the toe in. If you are towing a race car then you should know how to measure and set the toe.