Absent a court order to the contrary, both parents are equally entitled to the child. Only a court order is given the effect of the law; so for example, if the child is not in any danger and the parent that wants the child calls law enforcement, they generally will not get involved absent a court order (if there is a court order they will have the parent that is entitled to possession, per the terms of the court order, have the child) unless it is required to keep the child safe.
So most parents will start the legal process so they are aware of what their legal rights are. If there is a written agreement, the court will take that into account, but they are not required to rubber stamp that - rather they will look to ensure the best interests of the child are being furthered by the agreed upon arrangement.
Then once a court order is entered, if a parent violates the court order, they can be held in contempt. Contempt is a willful and knowing violation of a court order, and can result in the award of legal fees, fines, even jail time. If a parent continues to frustrate the other parent's parenting time, that can be grounds for a change in custody (based on "parental alienation").
relevant statutes here:
Factors the court will consider (you will see they are very broad and give the individual judge great discretion):
The age and physical and mental condition of the child, giving due consideration to the child’s changing developmental needs;
The age and physical and mental condition of each parent;
The relationship existing between each parent and each child, giving due consideration to the positive involvement with the child’s life and the ability to accurately assess and meet the emotional, intellectual and physical needs of the child;
The needs of the child, giving due consideration to other important relationships of the child, including but not limited to siblings, peers, and extended family members;
The role that each parent has played and will play in the future in the upbringing and care of the child;
The propensity of each parent to actively support the child’s contact and relationship with the other parent, including whether a parent has unreasonably denied the other parent access to or visitation with the child;
The relative willingness and demonstrated ability of each parent to maintain a close and continuing relationship with the child, and the ability of each parent to cooperate in and resolve disputes regarding matters affecting the child;
The reasonable preference of the child, if the court deems the child to be of reasonable intelligence, understanding, age, and experience to express such a preference;
Any history of family abuse or sexual abuse. If the court finds such a history, the court may disregard the factors in subdivision 6; and
Such other factors as the court deems necessary and proper to the determination.
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Information provided is for educational purposes only. Consultation with a personal attorney is always recommended so your particular facts may be considered. Thank you and take care.