"When dancing (or indeed standing and walking) the easiest way to 'engage' this muscle is to try to pull your rib cage up and away from your hips. Your body will instinctively use the transvers abdominus to do this.
Incidentally, sit-ups exercise different muscles, which are on the surface and don't really play a part in posture."
Sorry Phil, but you've got the wrong muscle. The muscle you are talking about is important in standing erect, but that is not the challenge in ballroom dancing beyond the very beginner level. Instead, because of the weight position soon developed, the actual phyiscal challenge is to apply the muscle opposing the one you mentioned.
The muscles needed are the surface abdominals, because the task is to keep from bending backwards. And your lower ribcage should be pulled firmly down and not allowed to lift. The curvature of the back that is desirable occurs much higher, in the chest rather than the abdomen.