My ex recently remarried and his new wife posts pictures of my kids on her social media and I am uncomfortable with that. We have shared custody but I have primary custody as they are with him less than a quarter of the days of the year. Am I legally justified to ask her to refrain from posting their pictures online?
You can ask her, but she doesn't have to agree. Unless there is a provision in your divorce decree regarding social media, either one of you can post whatever you like.