Sway bar or Steering stabilizer?

You dont say what year or chassis but if ifs try some free stuff. Weigh coach on four corners and set tire pressure accordingly.
Look for any play in front end parts such as inner and outer tie rods,bell cranks,idler arms,steering box. Do you have air bags inside coil springs? Change sway bar bushings to poly ones. A rear track bar will help with the tail wagging the dog effect.
After checking all front end parts a steer safe or safe t plus.

You would probably be better served by adding a Track (Panhard) bar to both front and rear axles. These keep the axles and chassis tied together laterally, and reduce side-to-side play which causes your coach to be a "handful". Do a search on Google for "rv track bar".

I just had a new steering stabilizer shock put onto my F350 and it drives like a dream instead of a nightmare again. When you start fighting the steering wheel back and forth to hold a straight line, look to your stabilizer shock first and replace it. My old one lasted about six years.