are you sure the attachment is being propagated? on the client set a debug key on the PlayerCharacter to print the result of GetOwner()
if you make a function on the Client that disables the Controller and put them in the seat, and trigger that function does it have the same behavior?
are both instances running on the same system, or are both instance running on separate systems? if these are on the same system, if you give the Client focus and not the server does it jitter at that point?
is this happening in PIE, or in a Packaged version?