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I can understand モンスター娘 and 日常, but I can't understand モンスター娘のいる.
いる means " one be there" in this case, so モンスター娘のいる日常 means " ordinaries which the monster girls are there".
This "の" is used instead of "が" which is set behind a subject.
Literally: Everyday life in which monster daughter exists.
Commonly: Everyday life with monster daughter