A Twofold Tale

Two pairs of twins are born in different families; one pair are boys, and one are girls. One of each of the two twins dies, leaving only one boy and one girl. In a parallel world it is the same except that it is the other twin who dies. At one point in each of their lives a paranormal event happens which makes their memories switch places with their twins, so each of them replaces themselves in the body of their twin in the parallel world. The switch turns out necessary for the fate of both worlds.