I am visiting my mother and sister in Hawaii and my children and myself want to stay and live here. I will have a job with my family business, a much better life for my kids and a support system which I currently do not have. My kids are 7 & 11... can I stay here legally and provide a better life for my children?

Your forgot to mention why you are even asking. The father of the children objects? Please start at the beginning with all the facts.

Unfortunately you have not related the facts needed to answer you. Since you asked this under Family Law, we can guess that this has to do with a custody issue.

1) Are you and the children US citizens?
2) Are there any court orders that provide the other parent with custody and/or visitation.
3) Where is the other parent?