Yes, I am against abortion. Yes the federal government has the authority to regulate abortions in federal hospitals. I do not understand your question of whether the federal government has the authority to regulation abortion in foreign policy. Foreign policy relates to the relations between sovereign nations.
The Mexico City Policy requires all non-governmental organizations (NGOs) that receive federal funding to refrain from performing or promoting abortion services as a method of family planning with non-US government funds in other countries. The policy has not been in effect since January 23, 2009. Since 1973, USAID has followed the Helms Amendment ruling, banning use of US Government funds to provide abortion as a method of family planning anywhere in the world.
The policy was enacted by Republican President Ronald Reagan in 1984, rescinded by Democratic President Bill Clinton in January 1993, re-instituted in January 2001 as President George W. Bush took office, and rescinded January 23, 2009, 2 days after Democratic President Barack Obama took office.