The weight distribution hitch shifts weight to the front of the TV by adding stiffness across the hitch. It also add weight to the
tires of the trailer as well. The proportion is roughly equal to the distance from hitch to the front and the hitch to the trailer
axle. The research indicated that the majority of the stabilization is due to the shift of the weight to the trailer axle. (see sited information above).
The shift of weight to the front of the TV will tend to make the car understeer more which is a good thing towing.
Adding the air bags will stiffen the rear end which will raise the resonant frequency of the back of the TV and should be accompanied by stiffer shock absorbers which will also dampen the oscillations at the rear.
If the resonant frequency of the trailer coincides with the resonant frequency of the TV the result is the undulating ride experienced.
The fix is to shift the ride characteristics of the tow vehicle out of this range with the airbags. Their effect can be removed by deflating to 5 psi when not towing.
These will also level the rig and again research has shown that a large part of the loss of stability is the lowered roll center of the combination and the unfavorable roll couple when the rear end sags.
The easiest fix would be to add air shocks if available for the Santa Fe or air bags if not.
Of course a WDH could be added, but it seems overkill on a
Trillium 1300 at 1500 lbs and (I assume 13').
Here is a post on air bags from another forum:
Air Shocks - Hyundai Forums : Hyundai Forum
Here is what I found on an adjustable shock absorber, but according to the description modifications may have to be made for it to fit:
Rancho R38RS999292 Shock Absorber and Strut Assembly | Auto Parts Warehouse
Here is a link to Monroe:
MONROE SHOCKS & STRUTS :: e-Catalog
There are few choices for the Santa Fe available.
The handling is one of the reasons I went that another VW Sportwagon to tow my 16"
Scamp. The car is well damped with and without the trailer.
By the way most of the old dat form the studies on the interaction between trailers and cars is still valid and if it is actually read may add some understanding the the dynamics involved.
You cannot digest the data and tests in less than 22 minutes.
The dynamics of the trailer has not changed at all in the last 35 years and without a doubt the cars have improved quite a bit so the handling should be better. The interactions are very much the same when adding the trailer to a better handling car.
My experience with the VW has proven this to be the case. A poorly suspended TV is will not get better with a trailer attached.
Your experience may differ.