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if by "win" you mean be awarded joint custody, you would ordinarily just need to back up what you have told me here today. Custody orders are made in the best interest of the children. You have two children who you have been actively involved in the lives of for their entire lives. They are grounded in their community, they probably have friends, and Hawaii may be all that they have ever known. It is very seldom in the child's best interest to uproot the child, and move them out of state and away from the other parent, especially when the child has an emotional tie to the parent. I obviously have not heard mom's side of the story, but, based on what you have said, you would have nothing to worry about.
Let me know if I may be of further assistance. Thank you.