An attorney friend passed on this 2013 article on possible conflicts when U.S. Supreme Court Justices hear cases involving law firms that have their family members on the payroll.
The Court did establish a policy in 1993 to handle this matter. Under that policy, justices would not ordinarily recuse in cases brought by their relatives’ firms, unless the relative is lead counsel or the outcome of the case would affect the relative’s partnership share of the firm’s income.
In the case of Eugene Scalia, son of Justice Scalia who will be hearing BP’s emergency request to suspend claim payments, Gibson Dunn, the law firm representing BP, wrote a letter to the court in 2003 stating, “Until further notice, income from the firm’s Supreme Court litigation will be excluded from Eugene Scalia’s earnings on a permanent basis.”