I know about Oedipus complex.
- What is it called when a mother has sexual desires towards her son?
- Is the term reserved for single mothers or does it include married mothers?
The term "Oedipus complex" refers to a son's desire for his mother (very simplified).
The corresponding construct, denoting the desire a daughter might feel for her father, is called the "Electra complex" (the term was introduced by C. G. Jung but rejected by Freud, so it does not really exist on the same level of fundamental concepts as the "Oedipus complex"; Freud has been criticized for building his theory almost solely on the observation of male childhood development).
I am not aware that there is a term for a parent's sexual desire towards his or her child in psychoanalytic theory. The Oedipus (and Electra) complexes are considered normal stages during any child's psychosexual development, while an adult's sexual desire towards any child is considered deviant. To my knowledge, Freud did not much think about the adult perpetrators of incest at all, he was mostly interested in the role that the child's experiences had for his or her adult personality. So while he was aware and reflecting on the incestual experiences of many of his patients, his focus remained on them.
There is of course the term "pedophilia" for a sexual interest in children, but that is not a specific psychoanalytic term, and it does not make assumptions about the gender of victim or perpetrator. Related concepts are other chronophilias such as hebephilia, ephebophilia, partenophilia etc. These terms are used with slightly differing meanings by different authors (there is a graphical representation of the usage of some terms in the German Wikipedia article on hebephilia, which will give you an idea of the differences even if you cannot read the description), so even outside psychoanalysis it cannot be said that there is a clear term for perpetrators of a certain gender desiring victims of a certain gender and age.