R.K.
this is the problem about just having a mutual agreement and not going through the court. If you both agreed you could have met with a mediator and signed the agreed upon agreement because the new girlfriend or boyfriend can cause nothing but trouble. My ex's girlfriend is like this she thinks she needs to control everything that goes on I am so happy that we already had a court ordered agreement before she came into the picture because I can't get anywhere with my ex now.
As far as claiming my son hubby claims him because in order to claim a child as a dependent they must live with you more then 50% of the year so I say if he does not want to help you with the extras anymore don't let him claim her he technically can't since he only has her every other weekend.