There's no panhard rod in the rear, unless you've added one like some

 

I wonder if you get more wander when you wander off road than when wandering down the road?

 

assuming you mean in back of axle......panhard is to keep axle in alignment with chassis. the bushings on that allow for articulation in relation (it has some swivel to it). this should be a smooth operation....if your axle wants to go a certain way and your junked up blown out bushings will let it........it can
a lift can put the orientation of the axle and body/chassis out. (axle could now be centered to one side) an adjustable lets you pull it back in.

 

I think a good start for me would be to learn what all these rods are and what they are called.

 

I'm starting to think its the new tires. Set your pressures to 40 PSI all around and Give the tread time to wear in.

 

Dusty actually suggested that in a other post. I have put over 300 miles on the new tires now so that is why I am revisiting the issue again.

I changed the pressure from 32/36 to 36/40. I guess it seemed to help some.

BTW, What the heck is this chalk test?

 

It goes front the front-

drag link
panhard rod
axle
track rod
2 radius arms that go from the axle to the chassis in line with the vehicle

then the rear is 2 radius arms like the front
axle
then watts linkage(or panhard if you've added one)

 

chalk test ...gotta be a vid out there. but I draw a chalk line across the tire (not around it) on tread. drive on tarmac/concrete flat surface (doesn't take much to wear off chalk). look at line. if it wears off on the outsides first= too low psi. if it wears in center first= too much psi. if it wears off evenly = bout right.
but tire bulge do to rim tire widths can have an effect also. there is a math equation to plug into to get recommended psi also......but I suck at math

that pict shows too low -too high - good.....chalk wear would tell you this

 

So, If I were to try the radius arms, I would just replace the front? What issues does a lift cause with the rear radius arms. (Got to learn this some time)

 

I would go back to your OP, the alignment shop says you have a bad part (they have the tools to find that bad part). Have them fix it. Or take it to another shop and have them diagnose what is wrong. Get a second opinion.