I have purchased this app on my iPad and want my kids to be able to play it on their iPad. Can I load it on their iPad without having to purchase it again?
Yes. As long as that device is configured with the same Apple ID that you purchased the app with, you can download your iOS apps on as many devices as you'd like.
If you're planning to do so, I would also recommend setting up parental controls to ensure that your kids can't make any unauthorized purchases.