Translation:My wife is the mother of my children.
Good question. I read this: http://bit.ly/1eNpYeH
It says that the "personal a" is only used when a person is a direct object, as in:
"Jorge llama a María." or "Jorge llama a su madre."
In the Duolingo sentence, "Mi esposa" is a subject, "la madre" is a predicate noun, and "mis hijos" are the objects of the preposition "de"--in other words, no cause for the "person a" in this sentence.