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Hostile work environment is a very specific allegation to make, as a basis for quitting a job. You have to establish a long history of harassment sufficient to cause you fairly severe emotional trauma and you have to show that you'd made numerous efforts to resolve the issue with the employer, who ignored the request.
You haven't really stated facts that show that in this case, and unfortunately taking this off is not a legally protected activity. I certainly understand being close to extended family members, but the laws protecting medical leave don't extend that far, so the employer isn't breaking any law by refusing the day off.
If they aren't breaking a law, then it's not legally unreasonable to demand that you be there. Your resignation (or if they terminated you for missing if you didn't resign) would be a basis for arguing that you are not entitled to unemployment.
I'd still file though. Force the employer to put forward the argument and if you can point to anyone else at that office that has missed a day of work and was not terminated or forced to resign, you could get unemployment based on the employer's inequitable application of the rule.
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