I think that one distinct way in which Nathan shows his male domination is how the power dynamics of the family are governed. Nathan is the alpha and omega of everything. He punishes the girls without a thought, reflecting male domination. When Methuselah curses, Nathan presumes the girls taught the bird and thus are punished to write out lines. As their time in the Congo continues, Nathan becomes more forceful and determined to press on, to "save Africa for Jesus." He increasingly alienates his family, and in doing so, establishes that male domination that becomes embedded in his character.
The narrative fleshes out Nathan's character to show that his own fears and guilt from the war filters into his assertiveness and domination, to a point where he believes in the authenticity of his own beliefs regardless of anyone or anything else. This, of course, is combined with his own antiquated notions of women's capacity. He reflect this with his thoughts on women's education: "Sending a girl to college is like pouring water in your shoes…. It's hard to say which is worse, seeing it run out and waste the water, or seeing it hold in and wreck the shoes." The desire to "please" his notion of the divine causes him to be even more steadfast in his desires and attitudes, through which male domination becomes evident. The wedge between his family and him resides in this convergence of beliefs.