Is there anything that can be done to improve the way the car handles through bends when the surface of the road is rough and broken. On very smooth surfaces there is very little sideways movement of the whole car, if the surface is broken it generally seems to hop about a bit . Would better (faster acting) springs/dampers help this problem.

 

Unfortunately the problem you have can be made better however it will always compromise the cars handling somewhere else.

I'm not too sure what kind of spring and damper arrangement you currently have but very often people who own high performance road cars make the things far too stiff - with the consequence of poor ride or the cars ability to cope with bumps.

You say that the car is basically getting unsettled mid-corner by road imperfections. Does your car have adjustable dampers and if so is bump and re-bound adjustable separately?

If you don't have adjustable dampers then you can't investigate if changes here will help. The only real solution is to perhaps make the car more softly sprung - although again you will have to buy new springs. Ate the springs the standard item?