Which kind of relationship exists between mother and daughter in Mourning Becomes Electra by Eugene O'Neill?

This play is an "updated" version of the Greek Tragedy
Electra.  Both Sophocles and Euripides wrote plays about this
daughter of King Agamemnon, who was killed by his wife Clytemnestra upon returning from
the Trojan War, because Agamemnon had killed their daughter Iphigenia as a sacrifice to
the gods, providing the wind his ships needed to sail to
Troy.

So, Lavinia and Christine are patterned after the
characters Electra and Clytemnestra of these Greek Tragedies.  Their relationship is one
of complete lack of understanding, one for the other's situation, as was true for their
Ancient Greek counterparts.  Lavinia sees Christine's new love as a betrayal of her
mother's relationship with her father, and she, like Electra idolizes her military hero
dad.  She also harbors a deep desire for revenge upon her mother for killing her
father.

Between mother and daughter, there is also
competition for the love of Christine's son/Lavinia's brother, Orin.  This signifiesa
use of the psychology of Freud and and sense of incest in this modern play that did not
exist in the Ancient Greek texts, since this sort of psychological analysis of
characters was not invented until the early 20th century.  The terms, Oedipus Complex
and Electra Complex, however, are useful in examining the familial relationships in
Mourning Becomes Electra.

For more on
the mother/daughter relationship in this play, the Greek Tragedies
Electra and the Electra Complex, please follow the links
below.