The babies were conceived in a lab using eggs from an anonymous donor and sperm from Sean Hollingsworth, the partner of Robinson's brother, Donald Robinson Hollingsworth.
They were born in 2006. Robinson later sued, claiming she was coerced into the surrogacy arrangement.
In a decision made Dec. 23 but released this week, Judge Francis Schultz said that she is the children's legal mother and can seek primary custody.
The judge relied heavily on the New Jersey Supreme Court's 1988 ruling in the famous Baby M case.
Information from: The New York Times, http://www.nytimes.com