There are guns in the sky already. They were installed during all those "Secret Military" space shuttle missions in the 80s.
The Air Force has handled "space" issues since the first rockets in the 50's. Space is air warfare. Trump probably did not know that or care. He needs to have his own branch. Also there are already treaties about the sharing of space which challenge a space force. It is not meant to be defended by one country but the UN as a whole since space is shared by all. At least they felt this way when space travel was new. Depending on another country (many of whom has socialist governments) does not sit will with the nationalist view of Trump.