I think that the "wobbling" you mention is caused by the difference in the track of the Fiat camper chassis - the rear is wider than the front. This becomes noticeable when you encounter ruts caused by heavy vehicles in a well-used road, the front and rear wheels both try to pull into the rut but as they are not in line they cause the vehicle to "wobble". Doesn't have to be a deep rut either, and a long overhang would make it worse. Obviously it shouldn't happen on other "straight" chassis that don't have the wider track at the rear.
I don't think there is a cure for this although I, and many others, have fitted air-assist to the rear springs and it has transformed the handling. It's a relatively easy fit, no major dismantling and could be achieved by a competent DIYer in a couple of hours, although I got Dave Newell to fit ours whilst he was doing other improvements.
As the Pilote website says your van has a "wide CCS" chassis I'd guess that, yes, you may well get that effect. I counteract it by moving slightly left or right of the worn part to get the wheels on lesser used surfaces. Incidentally I've heard incorrect tyre pressures can exacerbate the problem. Check you're running at the correct inflation - plenty of advice elsewhere how to find out the numbers.
As for cost I believe mine (a few years ago) was around £350 but there are a number of different manufacturers - search on here or elsewhere for rear air-assist suspension kit.