91 Bravada Rear Differential Problems

The rear differential is locked up side to side. On a tight turn right or left on gravel or sand, I can hear and feel the inside tire scuffing, not being released. With the car off the ground, the left and right tires won't turn independently. I've replaced the oil with the recommended type.

Does anyone have experience with any additive that might help? Or any other relevant experience?

It's ok,
Your Bravada has a limited slip rear differential.
Up on a lift, both rear tires are not supposed to rotate independently, they're supposed to be connected and rotate the same direction with the transmission the Neutral and be locked together when in Park. It has alternating steel plates and clutches that are held tight together with a spring inside the differential housing. There's an additive in the gear lube that lets these pieces slip a little smoothly but in time it wears out and has to be replaced. Since you've replaced the gear lube already, now is a good time to add the additive, commonly called limited slip gear additive and available at most chain type auto parts stores. Follow the instructions on the container, pour it in and in a big parking lot, go in circles, left and right a few times to spread the lube on the clutch/steel surfaces. It'll settle down quicker that way.
Did you know that limited slip additive used to be made from whale oil? They make it from petro-chemicals now...at least in the USA.

I'm sorry but we gotta problem Snoopybear,
I didn't know but it looks like our Bravada's have a locking rear differential meaning under certain conditions, the axles are mechanically locked together which is cool when one of the rear wheels completely looses contact with the ground or in a really bad slippery situation but when everything returns to normal, it should return to an open/freewheeling style of operation.
There's a governor with flyweights and a spring, also a cam plate and I haven't worked on one yet.
I'm not sure I can explain it since I can't see what you'll see either.
Unless it just started running smooth, the rear cover will need to be removed to check for broken parts. I believe a Factory Service Manual is necessary to get the info & pics to make repairs.

Thanks for the heads up Maxwedge!