Your child's father cannot require that you move back, but he may attempt to initiate a modification (or contempt -- depending on the circumstances) action to seek a change of custody and/or visitation. In addition, if the custodial arrangement changes, child support may be altered to reflect possible higher expenses for travel, etc.. I advise that you speak with a family law attorney here in Georgia and provide them with the court order. Good luck.
I know this must frightening wondering whether or not your child's father can force you back to RI. The good news is he cannot force you to move back to RI. However, he may attempt to initiate a custody modification action to seek a change of custody and/or visitation. I agree with the other attorney's answer, speak with a family law attorney here in Georgia. I handle family law matters and offer a free 30 minute consultation. Feel free to call me (770) 9124-8155.