The word order here seems a bit confusing. If we're specifying a timeframe, 'Dan' is in the wrong place for the typical word order, isn't it? If it's used more like a conjunction, I would expect the translation to be "Then they would go to school" as, perhaps, a response to "What if it were a school day?"
No, that would be "dan zouden zij naar school zijn geweest". Sorry, I'm not a linguist, so I don't have a more grammatical explanation.
It's more like "After that/If ... happened, they would go to school." instead of "Back then, they would go to school."
Like 'Als het sneeuwt niet...,' a familiar conditional from winters my childhood.