Somehow I doubt there was a proper 4 wheel alignment recently if it
acts as you describe. Look for a disintegrated bushing and/or lost
shims in the leading pivot of the rear trailing arms. The really bad
problem there is the frame can rust out in that area, major repair
time/cost. As a side note some shops I've seen will bend the radius
rods rather that wade into correcting the adjustment points that rust
badly, they should be straight.
If you start on the brakes do the complete job, if not, you are only
going to be back in them again when you don't want to be.
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