I have a 93 Pace Arrow, virtually identical to your Southwind since my 93 is built on a 92 frame. I had the same problem with mine when I first bought it (used). I replaced the old bell cranks with two new SuperSteer Bell Cranks from Camping World. I also added a steering stabilizer to the front end. I had the CW shop in Elkhard install mine but if you are mechanically inclined and have the tools you could install them yourself.
While this hasn't totally cured the problem it has helped immensely. Much is the problem is caused by the long overhang behind the rear axled, unless you have a tandem axle.
A friend of mine has the tandem rear axles on his 37 foot 92 Southwind and he has no wander problems at all.
Woody