I would just go to the airport early (promptly?), perhaps there is a blocked seat, or they will eventually need to unload someone. If nothing else I presume they will need to relocate people on the plane so that your family can sit together as well, i.e. to supervise the kids

I don't believe Cathay would split a family (and certainly not leaving one kid behind) so I suspect they would prefer to offload someone else rather than 7 of you (and if your status is really Diamond it makes it even less likely to happen). I wouldn't be worrying that much, of course this does let you make it clear to which one of the kids is not in the good books at the moment and therefore has no seat :P