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You will want to petition the courts for custody based on the best interest of the child. I would advise you to hire a lawyer as they can get a emergency hearing in quickly and see if the judge will grant you custody based on the father not spending adequate time with the children. As far as his responsibility's these will not change with a full custody order. He will still be required to pay child support and such. The visitation may change some but he will still be granted visitation as well.
If this is not a possibility to hire a lawyer you will need to fill out the forms at the following link: Divorce Source: State Specific - Modification Forms for Custody ... Fill them out completely and submit them to your local clerk of courts office with the filing fee's. The clerk will help you get the paperwork needed to serve the father and will set up a hearing for a custody order.
I wish you the best,