Hello Mike,
Twin axle trailers prefer to travel in a straight line, because of the two sets of fixed wheels resisting turning. By this factor alone a twin wheeler will tend to be more stable than a single axle model, but as your respondent 'Mike' says twins can still snake. I regularly tow trailers of both twin and single axle configuration, and it is quite noticeable that the well balanced twin axel trailer tends to transmit more reaction to the tow vehicle: I believe that as the first axle hits the bump, the trailer tries to pitch upwards, and actually tries to lift the tail of the car, but when the second axle rides the bump it tends to pitch the trailer down increasing the load on the tow hitch. This motion makes the vibration in the car much more noticeable and jerky. The alko hitch can make a difference here in resisting motion in both the horizontal (yawing) and vertical (Pitching) which the leaf type stabilisers won't do.