Court visitation & other party planning to move...?

I have two kids that do not live with me. I've only signed their Birth Certificates since they been born. Both kids currently live with their mother and grandmother. We all live in Florida and eight miles a part. I often visit them when they allow me to. I am planning on getting my right as a father to have visitation. Why? Because I hardly see them for one and secondly since the mother of my children says she'll be moving out of state. The question is, if I were to get court approved visitation, does that stop her from moving out of state if I'm incapable of doing so?