Late night train Milan - Genoa

My 10 year old son and I are arriving Milan Linate at 9 p.m. and (bad planning) there is a furniture convention in town and $300 is the cheapest room I can find. Am I crazy to consider traveling by train to Genoa that night and getting in about midnight (I am guessing)? I would pre-book a hotel close to the train station in Genoa... Thanks for any input!

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