Translation:I am sitting in between my father and mother.
Because you ignored the heirarchy used in Chinese language, men/elder coming first. Of course your meaning is the same.
I sit in between my father and mother - a common theme with all these Chinese ones is it's not taking into account how ambiguous tense/voice is, like present vs present participle (I sit between my mum and dad vs I am sitting between). Aditionally, 妈妈/爸爸 should really be mum/dad whilst mother and father would be 母亲/父亲