Welcome.
First off, you are going to get hammered on calling the Liberty a "car" even though, IMO, it's build like a car just with 4x4. Put a full frame under it, and then I too, will call it something other than a car
Sounds like you've got a worn part in the front end. Sometimes worn out tie rods will cause a front end shimmy. I'm not an expert, but it could be the pass side CV joint is locking up on you causing it to pull. My suggestion would be to take it to a trusted shop who does alignments/front end work and have them go over it with a fine tooth comb.
I think I've read on here too, if the ball joints are wore out on the rearend tri link, it can cause front end swaying, but not sure.
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'99 Tahoe, 3" BL, 285/75/16's , MT II's.
'05 Liberty Sport, -wifey's
'98 Poncho Fireturd, 3.8L, .....the purple pig!

