virtual visitation
n. Long-distance access to a child by a divorced parent using technology such as a broadband Internet connection and a webcam.
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With work and the school week behind them, Charles A. Mason III and his daughter, Arielle, who live more than 1,500 miles apart, prepared for their scheduled weekend visit. There was no packing involved, no plane tickets, no car rides or drop-offs. All it took was some instant messaging on their home computers and a little fidgeting in front of their respective Webcams, and father and daughter were chatting, playing checkers and practicing multiplication tables.

"It's funner than talking on the phone, because I can see him," said Arielle, 10, who lives with her mother in Longmont, Colo., but has regular "virtual visits" with her father as part of the custody arrangement her parents worked out after her mother moved eight years ago. "It's just like being in front of him, but with games and computer stuff added."
—Lynette Clemetson, “Weekends With Dad, Courtesy of D.S.L.,” The New York Times, March 19, 2006
Divorce put David List and his 2-year-old daughter on opposite sides of the Atlantic Ocean, and he worried that she would soon forget him.

She hasn't, though. List's divorce agreement guaranteed him "virtual visitation" — the chance to talk with his daughter through an Internet video connection — and he and Ruby Rose, now 5, usually connect at least twice a week. The chats between California and Great Britain sustain them in between their in-person visits, which come only a few times a year.
—Ann Sanner, “'Virtual' visits for children of divorce pushed in several states,” The Associated Press, February 28, 2006
2001 (earliest)
A Bergen County judge is expected to grapple soon with a new question of the Internet age: Can daily communication online, complete with live pictures and sound, help a child feel close to her father even if they live far apart?

A divorced mother, who wants court permission to move from Midland Park to California with her 9-year-old daughter, says yes. The child's father, who lives in Ridgewood, says absolutely not. …

The novelty of using "virtual visitation" to try to make the decisions easier caught the eye of the media in an instant.
—Leslie Brody, “Court may weigh merits of parenting via Internet,” The Record, January 14, 2001
The more formal term for virtual visits is computer aided custody sharing.