I wonder if they could stand next to each other in front of the mirror, and then one reach through past the elbow and grab the person over to the side and pull them through to "swap sides"...
@Maea they're never actually on opposite sides of the mirror, otherwise it would be quite painful when they're halfway through and occupying the same physical space as their mirror counterpart. So either there's actually more than 2 parallel universes or the room the mirror is in is some sort of liminal space.