Interesting. I've always assumed I had to be present when extending my wife and kid's dependent extensions. Would be great if this is not the case! Please let us know if you're successful.
When YOU cancel your Extension (if that is want you have) you can buy a 7-day 'extension' for 1,900 baht to give you time to organise your departure. Otherwise, you have to leave on the day you cancel your Extension.
They can get an O visa like anyone else, if they meet the requirements (my wife did this). But as Tod Daniels says most just do border runs every month (or seemingly overstay!)