We’ve traveled with our kids for many years. Finding a center, who will let you dive, while the kids stay on the boat can be difficult.
Also consider this: would you be happy diving, while your kids snorkel somewhere else? I would not even consider that - unless there was a private snorkel guide (we did this in Komodo a few years ago, when our youngest was 12.)
What we have done during the years: hired a sitter (while kids were young), take turn diving, so 1 parent is always with the kids. Leave kids at resort - in room with plenty of dvd’s (before iPad/iPhone etc) or at kids club.
At 10 both the older got certified- our youngest has problems with the eustatic tube and still can’t equalise.
My best recommendation with kids 10 and 12: get them certified and diving with you (if you feel they would be mature enough of course)