Can a child choose which parent that they want to live with?
NC Custody: 1) During separation period, if my spouse moves out, can she legally contest and have child partly live with her? Or can the child legally remain where she is until the separation period is over and it is finally decided to which parent she lives with? 2) Does parental gender matter in custody? 3) After age 12 of the child, if she is (mentally) a mature child and chooses one parent over another, what is the likelihood (50%, 75%, 90%, 100%?) that she will be awarded to the parent of her choosing (full custody)?
If there's no custody order in place, your wife can take your daughter with her. However, it isn't clear to me that she could force your daughter to go with her, if she is moving out and your daughter wants to stay with you in the house, as long as you are interested in parenting.
Effectively, without a court order, the child might be the one who effectively makes the choice. Even if she were somehow moved against her will, sooner or later she would find a way back to the house, and potentially refuse to leave.
With or without a divorce, if there's a separation, either parent can petition the court for custody. It's quite likely that a 12-year-old, especially a mature one, will be asked for her feelings on the subject, but there is absolutely no way to put a number on the odds that her feelings will match the result, although increased age and maturity increase the weight that the court usually puts on the child's opinion (and if the court thinks the child has been "programmed" to give the parent's opinion, it will be disregarded -- or worse). The bottom line is always the best interests of the child.