Do I have no rights to my child if I moved to another state with my new girlfriend?

Your parental rights are not affected by your move out of state. If no orders have been entered, such as in a divorce, the visitation or custodial periods to which you may be entitled can be adjusted to permit time with your child during school breaks, since weekends are not feasible due to the distance involved.

Your wife is incorrect. You haven't lost any legal right to your child by moving, however, you have made it more difficult and expensive to visit with your child. Additionally, a judge may not want the child staying in the same house with your girlfriend present, especially since you are not divorce yet. Either of you can file for divorce but it will have to be done in Oklahoma where the child is. The court will order visitation for you. You can ask that mom meet you half way but she may object because you chose to move so far away. Usually the parents split the cost. If the child is in school, unless you get full custody, you will get visitation for most of the summer and the long holidays. Mom will have the child during the school year. If you want to visit your child and your wife refuses, it is up to you to file for divorce and visitation rights to enforce your rights. Otherwise, you are at the mother's mercy. Additionally, you should be paying child support regardless of whether a divorce has been filed or not. It would not look good for you in court if you have not been paying support.