If you can show detriment you may have enoght to change custody. You cannot get an order prohibiting her from dating, living with or getting married to anyone. The court also would not require either of you to notify of other occupants without there being a stipulation from each of you on the issue. In instances where the issue becomes more of a moral or best interest issue, mediation is a good alternative. The court is obligated to follow law which oftentiomes is a hand's off attitude with respect to interfering with a parent child relationship.
Mediation allows greater discussion of the issues.