I will argue with you, sort of working my way from the bottom to the top.
Women have a method to their madness, and it is best to not question that method. Lois' method is against motorcycles. No motorcycles, no minibikes, no mopeds, period. We may never know the exact reasoining for this situation, but it is a recurring thought that Lois expresses. I would not have connected this episode to Mini-bike, had you not brought it up. But it is Hal and Francis who realize that Lois, as with all women, wants to be correct. Their fake accident is an illustration of that belief. Maybe it never happened, but if Lois believes it did, then she believes she is correct, and that's important to women.
People make "promises" all the time, but what are these childish agreements that it becomes a crime to break? In the spur of the moment, you can agree to a great many things and not even realize, but in a child's mind, a promise is more than a mere agreement or empty words, even if it isn't signed in blood. Just the thought of the rocket ship was enough to satisfy young Dewey. Francis was about Dewey's age at the time, and this promise meant the world to him. When Francis' brain locked the thought away until he turned 21, it registered to Francis as greater than a promise. It had far more power and was far more important than anything else in his life. His father had an obligation, and Francis was obliged as well, thus his misleading his own wife.
Finally, I would like to point out another allusion to a past episode, when Reese and Dewey were asking Malcolm when his "waiting" plans had ever worked in the past. He mentioned a hampster and a girlfriend, the latter of which was certainly referring to season 3's "Malcolm's Girlfriend" and confirming Malcolm and Dewey's accusation. We saw it in the named episode, and we've seen it in other episodes as well. As the boys develop, their character traits remain much the same.
As a final note, another superb analysis by appanah. Great job!