Freud - Child Development Theorists

I am most curious about Freud’s Psychosexual Development.  It focuses on the classic mother and father relationship. But what happens when children have same-sex parents?  Freud claimed that you need a mother and a father to develop correctly.  To test this theory, I would find the classic “mother and father” relationship and see how those children developed.  While doing this, I would also study a family that is comprised of same-sex parents and compare the children of the two groups and see if they are different at all.  I would see if there were any noticeable differences in children who have two mothers or two fathers and the children who have both a mother and a father.