This is not a case where Kevlar will make any sense. You want the pedal board to withstand the stomping, not to hold the sharp fragments together if your son stomps it into pieces. Kevlar doesn't make the parts stronger, it just makes them fail saver in high kinetic failure scenarios (motorsport). Even if your son stomps right through the board, there won't be enough energy involved to make things flight around dangerously.
If you just want to make things more stable, Kevlar won't make any difference, because it is much less stiff than carbon, and therefore won't take much load up to the point the carbon has reached it's maximum elongation.