Do I have to allow my ex's new wife rights to my child?

I am a mother of a 6 year old. My ex and I divorced in TX, where the original order was written (for both visitation & support), then I moved to NC and he moved to FL. We were both active duty military, but he stayed in while I left the service to be home for my daughter. I switched to an Air National Guard component and do not deploy (lucky!). A year after remarraige, he sued me for full custody. It was denied but the judge orderd a new, NC order be entered. The order basically says the same things: he gets visitation for spring break, summer break, Thanksgiving in even years, Christmas in odd, and New Years in even.
However, I noticed something extra: “The minor child shall be with the Plaintiff during any of the Defendant’s overnight deployment on weekends; that if the Plaintiff is deployed, Plaintiff’s wife may exercize Plaintiff’s periods of visitation.” (He is the Plaintiff & I am the Defendant.)
Is this right or allowed under statutes? I haven’t been able to find it supported anywhere. The babysitter I had was a certified medic! I proved all of his accusations as false, I showed that she was well cared for, that I allowed and encouraged interaction with her father and her paternal grandmother. His mother even gave testimony saying she got to see my daughter more often when with me than with her own son! This seems to be the judge stating who is going to be a babysitter of my child, which is unwarranted.
What I’m looking for is a second opinion: Is this allowed? Can I appeal it? Will it be required to go before the same judge that wrote the order or can I get a different judge? I would hate to go before the same judge stating that I have issue with that judge’s order.

The court may enter any order that it deems is in the best interest of the child. It sounds like the judge felt that it is in the best interests of the minor child to spend your weekend deployment with family (even if a step-parent). There are different rules with regards for moving for a new trial under the rules of civil procedure. As for an appeal, the appeals court will not review the judgment simply because you are not happy. You will have to show that there was an error made. You should consider a consultation with an attorney to discuss if there were any errors made which would warrant the filing of an appeal or a motion for a new trial or similar relief at the district court level.

I really have no weekend deployments. I go about 45 miles away to show up for my drill weekend once a month, but go home every night. They also have state-certified & DoD certified daycare for people with kids. That was brought up in the trial. I also showed pictures (he accidentally e-mailed me the whole file he had of pics!) of my daughter standing looking very upset with the step-mom. You can tell she did not want to take the pic, but they are trying to get her to smile. One even looked like she was tickling her while smiling at the camera! (ha ha) So for a girl that loves taking pics to not smile with someone really meant something to me.
Well… I thank you very much for the response and for this site you have here! It’s been a big help. I will speak with my attorney and see what she thinks we can do.