My child wants to move out of state with her mother who has not provided her with the best living situation. I think that living with me is in her best interest. If this matter went to court, will a judge let the 12 year old make the final decision?
In California, minor children don't ever get to "decide" who they live with and spend time with; that's for the parents to decide, or for the court to decide if the parents can't agree. (That's why, legally, minors are minors, and adults are adults.)
The court will CONSIDER the wishes of a minor child in making a custody decision, IF the minor child is of an "appropriate age and maturity". There's not a magic number.
Judges will usually be MORE interested in the REASONS for the child's preference, than in the preference by itself, and will also be interested in how the rest of the child's judgment and decision-making looks (that's the "maturity" part).
If the rest of the child's judgment looks good and mature, he or she will get more of an ear; if, for lack of a better description, if a child is messing up in the rest of his or her life (poor school performance, law enforcement or discipline problems, etc.) he'll get less of an ear.
I've seen a judge tell a sixteen-year-old: "I understand you want me to change custody; you're messing up in school, you're in trouble with the law; so your judgment and decision-making, right now, looks lousy. No custody change right now. If you manage to get your act together, and you come back in a year, I'll take another look."
Judges also are often VERY unhappy with a parent who discusses the custody issues of a case with children who are NOT yet of appropriate age or maturity.