hi andy.
How can answer your question without sounding patronising or condesending ??, No idea but here goes anyway.
First no its not normal, although some movement of the van is to be expected a continuous side to side should be avioded as this is how snakes happen as the movement gets larger and larger until it gets uncontrollable.
Many things can cause this including tyre pressures, noseweight,van loading, ineffective stabilisation, worn rubber suspension, and wheel track,
The latter can be an effect on m/ways caused by HGVs rutting the surface the van then runs in the ruts but as the car may be narrower in wheelbase does not as the car moves left or right ever so slightly the van continues in and out of the ruts and appears to be swaying, conversly lighter vans seem to suffer the effects more than T/A heavy ones, and can at times be most unpleasant.
However there are things one can do to elevates some of the problems,
our bailey is the same weight as yours and was a pig to tow empty on the way back from the dealers at first I thought it was the towcars soft suspension (1.6 mondeo) but soon realised it was not.the van WAS swaying and pitching all on its own.
during the next few trips I improved things considerably by, changing the tyres to commercial 6ply steel C grade inflated to 42psi instead of the 32psi textile car tyres that were on it,
fitted a set of alko shock absorbers to stop the cupboards emptying all over the floor during transit,"due to harder tyres"
getting the old blade stabiliser out of the garage and using it along side the alko 301 hitch.
and after putting everything conceveable in the van required for a trip had it weighed on a weighbridge to asses the max weight of the van regarding MTPLM it was 32kg over weight as I had forgot the mover and had not deducted its weight from the user payload, after juggling round with the weight I had left and carefully loading the van ended up with a setup that was a pleasure to tow with,
even after changing the car to a lighter one (megane 1.9dti) and towing @ 96% it is a dream to tow.
I am not suggesting you go to all the lengths I went to but some of the information may be of help,
regarding the blade stabiliser in order for these to work correctly they must be set properly and in good order first strip down the blade and clean and rough up the forodo pads with fine emery paper re assemble and set the side movement to 35kg resistance with the aid of some scales, in use you may hear some creaking while turning this is normal and shows the blade is doing its job.
and lastly the condesending bit andy,
being new to this caravanning lark everything will seem complicated and a bit OTT but we all make misstakes even those of us with 40+years under the belt so keep trying, I once wrote on this forum "towing is like having sex the more you do it the better you get at it" keep practiceing and trying different things eventually you will get it right and then after a couple of years you will wonder what all the fuss was about,
colin