What you and your fiance need to do is read his divorce decree or other court order. Typically, there is a provision that is put in the court order that states that the parent getting the child can send another "competent adult" to pick up the child. The other party cannot contest who the other party is unless they have a valid reason why you would not be considered a "competent adult." Nevertheless, it sounds like you guys need to get this back in court if she is not cooperating with the child's exchange.
In regards to the police, having been a former police officer myself, I can tell you that they will not get involved much. They may do a courtesy report for you but they are there to enforce criminal matters, not civil matters. Court orders from a divorce are civil matters and only the court can involve itself in the middle of any issues.
For educational purposes only. No attorney-client relationship was created by this communication.