Mother was "moving" side to side in the back

[CCFMJL]

I took her and her dog to the vet yesterday but as she's only 4 months they sat the back. But going round corners and bends in general she said "this is hellish in the back it's as if it's fishtailing what's wrong". I didn't feel it but then I'm driving, when she's in the front she doesn't say it.

I don't hear or feel clunking ect from the back ie worn bushes shocks ect, what could it be.