Stronger core doesn’t always mean you have to go hard only on your six-pack muscles.
The abdominal obliques muscles, the ones who run through the sides of your core are probably even more important for your goal because they are the largest and biggest muscle group there.
The oblique muscles have a lot of functions – they help you bend the torso to the side, they are the ones responsible for rotating your upper body to the left or right, and perhaps most important, actually act to resist your torso from rotating, which helps to stabilize and protect your spine.
Here are some basic and not so hard exercises you can start doing at your own place.