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You're right to be questioning this request; don't spend too much time worrying about looking like the bad guy here. As a leader, you'll often be called upon to make some difficult and unpopular decisions. If that means having to say no from time to time as you look out for what's best for your parent group, Elly says that it's more than OK to be the bad guy.
There are far more reasons to deny this monetary request than there are to grant it. While it may come off as a nice gesture, coughing up $500 of your group's funds for a plane ticket for one parent is likely to raise more than a few eyebrows from other parents and even the IRS. Even if the request falls within your mission statement (for example, "promoting student achievement"), the IRS frowns on nonprofits using funds to benefit a single individual. (The exception is when a selection process is used, as with a scholarship fund.) So you can make the IRS look like the bad guys.
That's not to say that your leaders can't help out this mom in other ways. Your leaders could, for example, organize a bake sale or a spaghetti supper fundraiser at the school, then donate the proceeds from the event to the mom's cause. (Just be sure you've publicized the purpose of the fundraiser well in advance, and don't deposit the money in your group's bank account.) Good luck. And congratulations to that student, too.