I don't know the policy of charging for taking family along at the presidential level. My understanding is that the official pays out of pocket for anyone who does not serve an official function.

I know that state dinners in the White House are paid for by taxpayers but historically the family pays for their own private dinner parties.

Incidentally, since February 2006, per diem for Alaskan lawmakers has been $145. Not being counted as income, it is not taxable.