1996 e-350 xtl pass van vibrtion while turning

After I’ve driven the van for some 10-20 miles it vibrates through out the whole van when I turn left/right at low speeds. There is no problem at any speeds while going straight however. I’ve replaced both sides upper/lower ball joints, front wheel bearings, driver caliper, all the inner/outer tie rods, adjusting sleeve…etc, both rotors, u-joints(previous owner replaced them twice) new diff fluid, both rear drums with new pads. All 4 tires have signs of dry rot, but good amount of tread still on due to a lot of sitting. The van was sold as a 3.54 limited slip diff, but testing says its a possing traction. What am I missing?

Posi-Traction and limited slip are the same thing and the likely source of your problem. Differentials allow the drive wheels to turn at different speeds, needed when making turns. With a conventional differential if one wheel loses traction the opposite wheel will lose torque. A limited slip differential has a clutch mechanism that activates when the speed difference between the two wheel becomes too great. It keeps the opposite wheel turning. Rebuilding one requires special tools and experience. You might be able to purchase a complete rebuilt unit or replace the entire rear axle with a non limited slip from a salvage yard.