If my ex-wife and her fiance are adopting a pit bull terrier who comes from an abusive home, what are my rights to protect my children who live there 50% of the time?

Give your ex-wife an ultimatium -- get rid of the dog or you will file for full custody.  Depending on the circumstances, a judge might grant your request.  You should consult with the attorney who handled you original divorce to determine if your state considers this news danger a material change that adversely influences the well being of your children.