Can my ex wife post pictures of our son on her business social media page without my consent when I have full custody?

This question brings up many issues: 1. Copyright - who owns the right to use the pictures?  Generally, the photographer owns the copyright to a picture.  If the picture was taken from your social media then a DMCA take down notice should be effective. 2. What is the picture being used for - Your son has a right of personal publicity when it comes to someone using his picture for commercial purposes. 3. How old is your son? - Sometimes age can be a factor. Finally, you may want to consider hiring a lawyer to send a Cease-and-Desist letter.  While a cease-and-desist letter has little legal impact, the lawyer's letterhead gets the recipient’s attention.   This is a relatively inexpensive way to put the person on notice that you are not going to let these actions continue and that you are serious about pursuing your legal remedies.  It also tells the person that they could get in legal hot water which will cost them a lot of legal fees if nothing else.  This will often convince them to stop their evil ways.