A no contact order is not appropriate here.  A no contact order would prevent your spouse's ex from contacting you.  It would not prevent her from posting on the internet or speaking with others.  Generally, people can post what they want on the internet.  However, if your spouse's ex is posting things that are false, this could be defamation.  In order to prevail in a defamation suit, you have to show that someone said or wrote something false about you, that another person heard or read the false comment, that the person speaking or writing the false comment knew it was false and that you suffered harm to your reputation or economic damage as a result of this comment.   This would require you filing a lawsuit and proceeding through the formal legal process, which can be expensive and time consuming.  It is a sticky situation.  Depending upon what she is writing, I would ignore.  I think in general people reading her facebook page can likely see this is an ex spouse talking about a new spouse and it is just sour grapes.  Secondly, I suspect she is looking for a reaction from you or your spouse.  If you don't react, it may take the fun out of it for her.  If there are chldren involved, perhaps your spouse could approach her and ask her to stop as this is harmful and embarassing to the kids.  Good luck to you.