Work with your chain of command.
If you have a valid case* and state it well you can probably work something out. Make sure you cover all your bases: transit to/from the airport (work with sponsors or squad leaders), how you're going to get any missed school work done, etc., etc.
At the very least, maybe getting an extra weekend with out of bounds is possible. I doubt this would officially fall under the purview of e-leave, but it's worth putting up special request chit and giving it a try.
*I'm not trying to belittle you or say you're trying to be weaselly in any way, but, as I'm sure you know, mids have been known to be less than scrupulous to get away from the academy. When I was TAD over the summer, there was a mid who got caught telling his company officer that his mother was dying of cancer and he needed to go home when he really was just trying to go home for his girlfriend's prom or something ridiculous (surprise! he's no longer a MIDN).