When you work for the U.S. Government and your work is in DC, why wouldn’t you be expected to live there?  If you are in the military and you get orders, you move.  If you don’t move the family then you have to figure out how and when to visit “home” on your own dime.  That shouldn’t be any different for the SecDef.  Members of Congress and any staff need to live where they work.  If it costs money from the taxpayer to have them go “home” on the weekends (or any other time) then you make the sacrifice and just don’t go.  Live where you work, work where you live.  Period!