Sounds like your XW is a narcisstic sociopathic jerk. I think FaithIsBelieving must have married your XW's sister as his STBXW has similar behavior. They have no problem telling lies to get what they want at all costs.

There are some books that might be of help in dealing with her over the coming years:

Divorce Poison: Protecting the Parent-Child Bond from a Vindictive Ex

Joint Custody with a Jerk: Raising a Child with an Uncooperative Ex

If there is one saving grace, I have witnessed a friend and my brother, both with son's who eventually would not put up with their crazy mother's when they got into their teens. Both of them got full custody later on because of their XW's inability to control their anger towards their son's.