Martha Minow recently became dean of Harvard Law School. She also has been nominated by Obama to be a director of the Legal Services Corporation, the federal organization that provides civil legal services to the poor. She and her father both clerked for Supreme Court justices - Martha for Thurgood Marshall and Newton for Frederick Vinson.
http://news.muckety.com/2009/09/11/just-sit-right-back-and-youll-hear-a-tale-of-the-minows/20011
According to a story in the Harvard Gazette, Minow has been a member of the Law School faculty since 1981. She is a distinguished legal scholar with interests that range from international human rights to equality and inequality, from religion and pluralism to managing mass tort litigation, from family law and education law to the privatization of military, schooling, and other governmental activities. She is also a widely admired teacher who chaired the law school’s curricular reform efforts of recent years.
http://newsblogs.chicagotribune.com/chicago-law/newton-minow/
One day, when just a mere professor there, she [Martha] called her father at his Sidley Austin law firm in Chicago and recommended he hire the smartest student she'd ever taught. Barack Obama. And it was at the firm that he met another lawyer, Michelle Robinson. You know the rest.)
http://www.huffingtonpost.com/robert-j-elisberg/the-bizarre-world-of-nell_b_276441.html
Martha is married to Joseph Singer, the Bussey Professor of Law at Harvard Law School (teaching property law) 
Professor Joseph William Singer began teaching at Boston University School of Law in 1984 and has been teaching at Harvard Law School since 1992. He was appointed Bussey Professor of Law in 2006. Singer received a B.A. from Williams College in 1976, an A.M. in political science from Harvard in 1978, and a J.D. from Harvard Law School in 1981.
Nell Minow, the eldest, is an expert on corporate governance. As co-founder of the Corporate Library, a research firm, and Lens, an activist investment fund, her views are much sought after by business executives and board members, government officials and journalists.
http://news.muckety.com/2009/09/11/just-sit-right-back-and-youll-hear-a-tale-of-the-minows/20011
Nell Minow is married to her childhood sweetheart, David Apatoff, an accomplished Washington lawyer, who grew up two blocks from me. This lead to two children, Benjamin and Rachel -- which lead to the Movie Mom, 15 years ago.
Apatoff jokes that she picked two careers where she always gets to give her views. And she gives them with fearless honesty. How much so? Once when advising shareholders, she recommended they drop one of the Board of Directors. It was her father! (He'd missed too many meetings for her standards. When he explained to her his excellent reasons, she graciously understood his excuse -- and repeated her recommendation.)
http://www.huffingtonpost.com/robert-j-elisberg/the-bizarre-world-of-nell_b_276441.html
Arnold & Porter, LLP; Washington, DC
David Apatoff has decades of experience representing large technology companies on sophisticated contractual, regulatory, and compliance matters. He focuses on federal contract law, intellectual property rights, and international transactions in the telecommunications and information technology industries.
Mr. Apatoff’s experience with federal grants and contracts ranges from major defense systems to basic research at some of the nation’s premiere educational institutions. He has handled contract disputes, suspension and debarment proceedings, Defense Contract Audit Agency audits, bid protests, and investigations by the US Securities and Exchange Commission, Inspectors General, US Government Accountability Office, and the United States Department of Justice.
http://www.arnoldporter.com/professionals.cfm?u=ApatoffDavidB&action=view&id=1
Mary Minow is an attorney, a former librarian and library trustee, and a library law consultant with librarylaw.com. She has taught library law at the San Jose State School of Library Science. She received her B.A. from Brown University, her A.M.L.S. from the University of Michigan, Ann Arbor, and her J.D. from Stanford University.
Mary Minow is married to James ????????. I spent an hour looking for his last name---all to no avail. Mystery man!
This is a start, but have not seen any connections here to the Chicago "machine." --- perhaps more to be gleaned in educational philosophy and/or political ideology.