I know that the San Juan School District has an open policy. Meaning if there is room in the school of your choice then you are able to move your kids to that school. BTW, the district doesn't offer bus service if you plan to do this.
Like Sue said, I don't believe that there is a policy if you live in one district and wishing to put your kids in another school district.
I have seen in some cases, if a child lives with one parent living in the district (divorce, separated, etc parents) that child can go to that neighboring school. I have also heard of children going to a neighboring non-district school due to a program that an another district doesn't offer. EI - special needs children. I would strongly recommend contacting the district you live in and research the school.
If all else, you may want to move. Sorry!
Nancy S Bergman
Realtor - LSSC
DRE # 01893550
Lyon RE Downtown
2801 J Street
Sacramento, CA 95816