mother country vs country of origin

mother country and country of origin both are nouns.

Word	Noun	Adjective	Verb	Adverb
mother country	Yes	No	No	No
country of origin	Yes	No	No	No

As nouns, mother country and country of origin are synonyms defined as:

Other synonyms of mother country include fatherland, homeland, motherland, native land.

mother country (noun)	country of origin (noun)
the country where you were born	the country where you were born