[Jean-Paul]

The core is all of the muscles of the trunk (yes, abs are a part of that), back, hips, and glutes.

It's hard to say what you need to fix without doing a functional movement screen on you, but if you are toppling on a squat, I would recommend doing some unilateral work... Some bodyweight Bulgarian Split Squats. You might also lack hip stability, so some low cable adduction/abduction (balancing on the other foot with no external support, i.e. holding on to something with your hands). Throw in some low static bodyweight squats.

You may also have some lower leg stability issues. Again, hard to tell with the limited info.