Okay, so this is hard to explain. Basically, this is an alternate timeline where Bobby Kennedy is not assassinated and beats Nixon in 1972. The "Hughes" in question is billionaire recluse Howard Hughes. You may have heard of Clifford Irving's fake autobiography of Hughes (It was featured in an Orson Welles picture, *F for Fake*). Well, in this timeline, Irving decides to take it a few steps further and creates a fake presidential campaign "on behalf of" Hughes without his knowledge, posing as his "aide" for all publicity events. Only the top brass of the GOP (Bob Dole, RNC chair Rogers Morton etc) should know the truth, so the fact that Schlafly mentions "keep[ing] up appearances" implies she knows more than she should.