I see some RVs with extreme overhang at the rear. That could exacerbate any overloading because that's where the extra weight is likely to go.
If you have ever pulled a trailer that was way heavy in the rear then you know how important weight distribution is.
Acceleration shifts the weight even more towards the rear that's why the wobble kicks in.
Depending on the location of the tanks those could play a big part.
BTW, I consider those tires unsafe. Even if they were new, 4 to 5 yrs
puts them near the end and sitting all that time cannot be good.
I would replace them all. Rearrange your weighty items and go somewhere.