Flew HKG-HNL this summer. Unfortunately, I don't think that there are direct flights. I transited through ICN on Asiana. From HKG, I think your best bet (as others have said) would be to go through NRT or ICN. It's the 'closest' and most direct way to HNL if my geography serves me right. Our total travel time including the quick layover was about 13/14 hours. There are flight plans (that if all goes right) you can do it in ~12.5 hours and those go through NRT usually.
Flying to the continental US then to Hawaii is also possible, but with youngins, the backtracking and extra long flight doesn't seem like something you want to experience.
Me and my mom did HKG-ICN-HNL this past summer on Asiana Business via UA miles. You can read about my experience
HERE and
HERE if you want.