You'll have to find out your district's rules by calling either the new school or the school district office. Usually, you have to attend the school you're assigned to (which isn't always the very closest school which seems to be the case for you). But sometimes districts allow for inter-district "transfers". You'd probably have to fill out an application saying that you want your kids to go to the old school instead of the one you're (now) assigned to. If the old school has capacity they may allow it.
But again, the only way you can be sure is to call the school or district directly. Most school offices are opening back up about now for the new school year so you should be able to contact someone.