The age of majority in Michigan is 18. At that point, she can choose to live with whomever she pleases. Unfortunately, until then, you would have to get a modification of the custody or parenting time order before the child could live with you. You and the father could agree to a change in custody or parenting time and take this before the court. While such an agreement is not binding on the court, the court will generally enter the order unless it is against the best interests of the child.
If you and the father cannot agree on custody or parenting time, then you would need to make a motion for change of custody or parenting time, or both. To do this, you would first need to show (1) proper cause or (2) change in circumstance for such a change. These standards are very complicated due to the high volume of law interpreting these phrases, so I cannot go into exactly what that means. If you cannot show either of the above, then the court will not review the custody order. If you can, you would then be required to show that a change is in the child's best interests. Again, the "best interests" standard is complex and nuanced so a discussion of that standard cannot be had here. Suffice it to say, while the child's desire to live with a particular parent are taken into account in the "best interest" determination, it is only one of the factors considered by the court. But it can be persuasive in situations where the child is older and can articulate the reasons for wanting to live with one parent or the other.
I agree with Attorney Swartz's answer but will add that once you do show a change in circumstances, the judge may interview the child as to their preference how much weight is given to their preference depends upon their level of maturity and the basis they want to move.
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