My daughter is 14 and wants to live with me (father) but I only have visitation rights. Can she legally choose who she wants to live with?

Your daughter is a minor and still subject to the custody and visitation order that presently stands. What is usually done to change those orders is the parent that wants the change can bring a petition to modify the order and request to be the custodial parent.  Your daughter is old enough that a judge will give her the opportunity to express her reasons for wanting to live with you rather than her mother.  This is given great weight by some jurisdictions but the bests interests of the child is usually the standard. 

Judge's don't want to hear that children want to jump from one parent to another for superficial reasons like a nicer house, more money, more freedom, etc.  They won't make a change for those type of reasons but want to know that the change has to do to with fostering the parent/child relationship or removing the child from an unhealthy environment to a healthy one.  you should seek legal counsel in your area for help.  This is not an easy task and you will need guidance.