i went through a similar scenario with my nissan pathfinder. i bought it used and didn't check carfax. it had a damaged upper control arm and pulled hard to the left. the dealer and 2 "alignment specialists" raped me and didn't fix the problem. they only adjusted the "toe in" because that's easy, and not the caster or camber, which require some effort.
this link explains the theory pretty well:
http://www.ozebiz.com.au/racetech/theory/align.html
i found the specs in the chilton's manual and aligned it myself. i basically took the measurements off the good side (the side that had nice even tire wear) and made the tweaked side match.
as for the "only during acceleration"
hmmm
i'd guess something is loose, a ball joint or bushing is bad, and the torque of acceleration causes the geometry to change and it misaligns itself. do you also hear a clunk when you let off the gas?
good luck to both of you
there!
if i see this message again:
Hello fishhead,
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i'll be really mad