my instruction mention briefly about body sway.
I find hard to extend one side of the body without lifting the shoulder ...
Does anyone have any tips/exercise to get that done right ?

Thanks,

I find it easiest to engage my lats. Keep the lats pulled down (much like the lat pull machine at a gym,)and rolled in, then stretch from the bottom rib. Try to keep the sides as long as possible. Then again, you should do this in every dance -- those back muscles maintain your connection to your partner.

Unless you can use your hips, and, more importantly, your legs, you really shouldn't be able to generate too much of a tilt in the shoulders -- otherwise you did not have enough of a vertebrae stretch to start.