I think he wishes to pose the question could there be a flight regime where aileron opposing rudder results in one prevailing over the other. The answer is sure, and if such an airplane does not exist we can design one. Sort of like the Skycatcher before it crashed (twice), it had an undersize rudder and they realized it was too small and made it a bigger. The problem is more rudder means more weight, drag, and structures and there is no getting around some tradeoffs.
The basic engineering idea is that knowing how an airplane will behave is dealt with by
flight dynamics. You can develop an accurate numerical model of an airplane to see what it will do. The engineers are called stability and control engineers. There are a bunch of design coefficients you have to know, and some of that is guesswork, but you can see what a design will do or not do this way. This is also what drives flight simulators although it is usually called a
flight engine there.
Back to the question. If you have too small a rudder you can get an airplane that has excessive aileron authority and not enough rudder authority. Ailerons roll, rudders yaw and to a lesser extent rudder also affects roll. An exercise I sometimes have my students do is to take their hands off the yoke and fly the airplane back to the airport using only rudder pedals and thrust. It certainly can be done. Rudder affects bank secondarily, and thrust as you know controls pitch.
Think about the basic physics some. What are we doing here? We are after moving the airplane CG using control forces. What does the aileron-wing combination do? It shoves the CG sideways horizontally and holds up the airplane CG. That is linear force. What does the rudder do? It rotates the CG about itself. That is rotational force. Which is harder to do? There are two ailerons on a massive huge wing on the one hand, yet the rudder is a single flying plane mounted on a lightweight tail box. Think about it. The rudder has the far easier job here.
As far as certification goes, I do not know of any rules that apply to an opposition situation between rudder and ailerons. There may be one, I am not the be-all on this. Quiet a few aircraft even have coupled ailerons and rudder to prevent cross-controlling. Ercoupes and Stationairs come to mind, but there are many. Of course there are a lot of rules concerning spin recovery, crosswind authority, stall speed etc. for ASELs and in theory we can design any type of ASEL we want, including one with the ability to maintain rudder authority throughout any flight regime.
If the rudder is weak it isn't because rudders are impossible to make strong enough, it's rather easy to do. The more serious question is how will the tail deal with all the stress placed on it by this huge flight control hanging out there on a thin aluminum box. In truth it is not hard to make a tail that is strong enough to withstand just about any reasonable rudder force. The wing is what fails first. The Airbus Flight 587 crash was a special case involving composite construction and dynamic loading.
Getting warm, Spotta?