Translation:My mother is the wife of my father.
I don't know if your question (if it is a question) is about the original sentence (usually in Esperanto) or the translation (English) but my answer is more or less the same. The translation follows the structure of the original here.
I assume that the sentence is said in a culture that forbids polygamy, so the “patro” is allowed only one “edzino,” which therefore is “la edzino.” Since Esperanto does not have a saxon genitive (my father's wife) the article must be mentioned, just like in the English default translation (the wife of my father).
Disclaimer: The same situation would apply to the combination polyandry / father / husband / mother. I did not make the exercise.