The legal way to resolve disagreements between two unmarried parents regarding who will have the child when is to file the appropriate petition with the court.
The free mandatory pattern forms for family law proceedings in WA are at http://www.courts.wa.gov/forms/ . That site has links to instructions and self-help guides.
If the parents cannot agree on a parenting plan for their child, the court will make a parenting plan that is in the best interest of the child. With which parent the child will reside the majority of the time will depend on the particular facts of the parents. Keep in mind that if the court determines that living with neither parent is in the best interest of the child, the court has the power to place the child with some third party.
Given that the proceeding likely will be a contested one, it may be more efficient to hire an attorney.
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