Sonic dilatant egress.

Two, silica sand suspended water, puddles fill two open holes in the floor of your throne room.
Under each cavity is a taut stretched rubber sheet with a hole in its center just large enough to accommodate the diameter, (at full stretch), of a fully grown human passing through it feet first. From both above and below inaudible sonic pulses pummel the dilatant mixture causing it to remain rock hard and allowing both supplicants to approach as though walking on concrete.
In this case the woman on the left says agrees that yes the baby should be halved and each woman given her share of it. The woman on the right recants saying, "No, the baby is hers, I lied that it was mine, she can have it!"

You depress the button located just under your left armrest to disconnecting the power source from its emitter.