No. those two 처럼 have no differences in meaning. You can translate 엄마인 것처럼 해 줘 to “Please act like you’re my mom” as well for example. 것 (more precisely, ㄴ 것) is just a grammatical device required by 처럼.
Unlike English “like”, which can be used also as a conjunction and not just a preposition, 처럼 is a particle that always needs nouns.
So when it needs to combine with a whole clause “(네가) 엄마이다”, we transform that clause into a noun using that “ㄴ 것” first before giving it to 처럼.
The Language Level symbol shows a user's proficiency in the languages they're interested in. Setting your Language Level helps other users provide you with answers that aren't too complex or too simple.
Has difficulty understanding even short answers in this language.
Can ask simple questions and can understand simple answers.
Can ask all types of general questions and can understand longer answers.
Can understand long, complex answers.
This answer was given within 60 minutes of the question being posted.
How do you say "Hello" in Korean? Find out on HiNative!