Modern twin-clutch automated-manual gearboxes are proving very popular. This seems to be because they provide a seamless driving experience without the need for those pesky gear changes. For those of us still enjoying manual gearboxes, the key to good control when changing down a gear for a corner or hazard, is timing.
When approaching a corner, it is most stable to completely finish the braking phase before starting to turn. The gear change should occur late in the braking phase or just between braking and steering. This includes re-engaging the clutch to allow you to drive the corner. It also means you can revert to two hands on the wheel for the steering phase.
If you are struggling to get the gear changed and clutch pedal released before turning the wheel, try starting your braking a few car-lengths earlier and this should buy enough time.