If it is possible to stay for one more year than I would encourage a heart to heart talk with the kids. If one is excited to move, but the other wants to stay and graduate from their current HS, I wold say that the family should stay. If both are happy with the idea of moving, than I would go ahead and do so. I wouldn't take too long to move though, as changing states may change graduation requirements. This could leave them to needing extra units to meet state accademics.
If you REALLY need to leave for some reason, such as amazing job opp., and they want to stay, perhaps there is a family member that would be willing to care for them this year. You could pay a "child support" so to say to them for the year. I know it would be hard, but may be your best coice. My Aunt had to move (from CA to CO) during my cousin's Sr. year. When she went to regester in the admisions office they looked over her transscript and told her she would not be able to grad until the following Fall because she didn't have some of the ST required classes. So, her Mom put her back on a plane to come live with us for 4 months until she Grad HS. My Aunt sent a check to my Mom for about $200 a month (1991) to cover her daughters "food and allowance". My Mom never asked for it, but my Aunt felt that she should sense she'd be spending that money on her anyway.
Just some ideas. I hope it helps~J.