Islam is riddled with homosexuality, although it’s usually men trying to be like pretty women, rather than men trying to be ugly women. This is a very common feature of polygamous cultures.
The premise of the complaint in this situation is that the man is afraid his wife will have sex with the driving instructor, who is more-or-less physically male at this point. That says everything about the complainant’s opinion of himself and of his wife.
After all, what kind of Muslim “man” lets his wife drive?
I don’t think Islam is as riddled with homosexuality as the West. I think the religious concept of separation is involved much more than lack of trust of the wife. Many religious groups practice separation from the world to try to limit the damage it can inflict on them and their families.