Coilover's replace the strut's, so I believe you mean strut brace's.
If they are bounceing, then they are too hard, and upset the balance of the car. If you have damper adjustment, set it on the softest setting you can, and see how it handles. If the coilover's are from Japan, they are too hard for Irish roads.
Replace the droplinks, front and rear, uprate the front anti-roll bar bush's, and fit a 22mm or 24mm adjustable rear anti-roll bar. Fitting an anti-lift kit improves corner turn in and keeps the inside wheel planted a lot better through a corner. A good suspension set-up and the car will be transformed.
John