I've done a few family trips in Indonesia and it mostly depends on a few things:
1. How old are the kids? Kids are easy to keep busy after a certain age. But I've seen a few 5-6 yr olds get scared when their parents go diving for a long time. I don't think it's fair to put the child caring on the boat staff, but depending on the boat, it's possible to pay the staff extra for that. Infants are fine, if they aren't cryers... but that brings up the bigger issue...
2. How are the parents? My god daughter was 8mths old, had a bit of a fever, and her mother had post-natal induced fit and demanded the boat be turned around in the middle of the Banda Sea. My god daughter survived, her mother still brings it up after 12 years and her husband is still useless, and he's the doc!
3. How spoiled are the kids? If they are demanding of attention, you won't enjoy the trip and will end up skipping dives. Eveybody's kids are angels in their own eyes, but this is an assessment you'll have to be honest to yourself about.
I'd do a private charter of a smaller boat and bring 2 to 3 families with kids. The kids can terrorize the boat while you dive. Oh and if there's a time to tip the staff in Indo, it'll be after a family trip, but somehow most liveaboards note that photog trips tip better than family style trips. Hmmm. Quite a few boats doing that in Komodo. A smaller boat like the Shakti does R4, except the boat isn't very childfriendly (shared small baths etc) but the staff are fun. You may also consider the Grand Komodo and Temu Kira for R4.