mother-in-law vs female parent

mother-in-law and female parent both are nouns.

Word	Noun	Adjective	Verb	Adverb
mother-in-law	Yes	No	No	No
female parent	Yes	No	No	No

As nouns, female parent is a hypernym of mother-in-law; that is, female parent is a word with a broader meaning than mother-in-law:

mother-in-law: the mother of your spouse
female parent: a woman who has given birth to a child (also used as a term of address to your mother)

Other hypernyms of mother-in-law include in-law, relative-in-law, mother.

mother-in-law (noun)	female parent (noun)
the mother of your spouse	a woman who has given birth to a child (also used as a term of address to your mother)