Quote - How can I get B to move just at the moment B gets shoved, and not before. I'm missing something obvious but inserting key frames isn't working for me. Eventually, B turns out reacting long before the shove (say at frame 30)

You'll need to use the spline break options and additional keyframes to make sure that figure B doesn't a) move until you want it to, and b) you don't get odd movement due to overshoot on the spline interpolation.