Greetings. Sole custody means sole decision making. Now, I will tell you that yes, you apparently (going only on what you say about the agreement) have the right to determine if there will be any visitation at all. But, please remember that if you do not allow him to visit, even if his new girlfriend/wife is present, then he could easily go to court and get a lot more visitation then you are currently providing.
As distasteful as his behavior is, it does not say anything directly about him as a father - at least not when your daughter is age 4. Thank you.
Janet L. Fritts
Attorney with Rosen Divorce
4101 Lake Boone Trail, Suite 500
Raleigh, North Carolina 27607
919.787.6668 main phone
919.256.1665 direct fax
10925 David Taylor Drive, Suite 100
Charlotte, North Carolina 28262
704.644.2831 main voice
704.307.4595 main fax
The response posted above is based upon the limited factual information made available and is not intended as a full and complete response to the question. The only reliable manner to obtain complete and adequate legal advice is to consult with an attorney, fully explain your situation, and allow the attorney sufficient opportunity to research the applicable law and facts required to render an accurate opinion. The basic information provided above is intended as a public service but a full discussion with an attorney should be undertaken before taking any action.