Unfortunately, なぶる is very rare in modern Japanese, except that the compound なぶり殺す is occasionally used.
I'm not sure about the exact nuance of "tormented by daily life", but if I have to find a transitive verb that fits this situation, I would choose 打ちのめす or 打ちひしぐ. The latter is mainly used in its passive form (打ちひしがれる).
There is no problem with using passive voice in a relative clause. But don't insert a comma between the noun and the relative clause.
And generally speaking, Japanese language tends to avoid inanimate subjects with transitive verbs. See this discussion, or examples here. If you can replace the subject with 少年, you can say this in various ways using 「思い悩む」「絶望する」, etc.