Te = applying logical, causal order to the external world based on objectively verifiable standards and measurements
Fe = harmonizing/unifying the external world based on the public cultural standards of behavior
private personal values
Fe is a form of Je, extroverted judgment, which deals with organizing the outer environment in order to, as I said, harmonize with cultural standards for behavior in whatever tribal group the Fe user identifies with.
You seem to be assuming that cleaning the house and arranging it methodically automatically invokes Te, but I would argue that this sort of physical organization of the physical world is just as easily performed from an Fe standpoint. It's probably something to the effect of, "My tribal group values having a clean house, so I clean my house."
If the questionable practice which the FJ is worried about actually is
the prevailing cultural norm in this context, Fe would lead us more toward sucking up our personal problem with it and just not saying anything. After all, it's the group's customs and cultures, the group's traditions, and the group's values that are typically more important than the FJ's internal personal qualms.
Anyway, I've never heard anything about extroverting judgment in neither the Te nor Fe form, and I think whichever of these is being "used" is dependent upon the person's motivation for it--does she place more value on the strategic advantage in applying impersonal causal order, or is it more important to her to harmonize with the prevailing values of the people and culture with which she identifies? Of course, I am sure she is aware of both advantages, but whichever is higher in her value system, whichever strikes her as the greater concern, is going to be the indicator of which function is at use. Cleaning the house could be an expression of Te or
Fe, or even another function, depending on why
your wife is doing it.