While tritype theory states: "research shows that the other types in the Tritype are employed for use when the dominant patterns and defenses are no longer effective. The Tritype is therefore usually only engaged when the defenses of both wings and all the lines of connection have been exhausted," this doesn't appear to be even remotely true according to my own research. (See: http://en.wikipedia.org/wiki/Tritype for more on the Fauvre's theory of Tritypes.)
Rather, "dominant patterns and defenses" are employed according to circumstances in one's environment. The primary (or core) motivation controls one's life destiny. It is accompanied by alternate motivations (psychological needs) deemed most appropriate for whatever particular tasks, such as, "I don't want people to think I'm a bad person," or, "I just want to be left alone."
Motivations that conflict versus those that don't conflict.
Your core motivation may or may not conflict with your wing-type's motivation. However, it does not conflict with tritype motivations founded within the other two Centers. So while my 4-wing will conflict with core 5, in its role as a tritype, 4's motivations do not directly conflict with 5's motivations, or even necessarily support them, just as emotion can separate from thinking, temporarily negating the motivating power behind thinking (which is to intellectualize or rationalize away the personal and social value of emotions or "feelings"). Thus the 5's defenses are circumvented and replaced by other motivations that are completely foreign to the 5's motivations due to the dualistic internal relationship created by them.
As far as I can tell, the Fauvres neglected to mention the role that the lines play regarding tritypes. If I have point 4 in my tritype, this leaves the possibility of moving to 2 or 1 when 5's motivations have been circumvented. If I have point 9 in my tritype, then likewise, this alternate motivating force can move to 3 or 6 when its motivations have circumvented those of the 5.
Various motivations can co-exist in the same psychological moment
While monistic Enneagram theory builds upon the theory of core motivations, human nature is, in reality, and at any given moment, infinitely more complex than this. But humans have a built-in desire to simplify all things down to a single formula, such as the 9 core motivations, or even a single motivation governing all humans, such as "I want to have control over my destiny (and as a corollary, over the destiny of others either directly or indirectly)." If we can learn to control this desire to boil everything down to a single principle, then we can force destiny to conform to our wills rather than vice versa.