I think that a lot of the tires that come with the trailer are just made to get you from the RV dealer to the tire shop. Mine would sway from side to side no mater how it was loaded or if it was empty. After a half of a season two tires blew within a couple of miles
I spoke to the tire guys and they said it's pretty common. In the end I got new tires and they have lasted pretty well. If I remember correctly the tires were only rated to haul the trailer empty.
It sounds like you have another issue though. I would certainly look at how you are tracking or if your axles are fubar.