Answer
Salam Dear Rahma,
Thank you for your sincere question and desire to seek the truth. May Allah make the path to truth easy on all of us.
Although this is not a fatwa, I pray that it helps shed light on the perfect justice of the religion of Allah.
First, it is imperative to stress, as you already mentioned, that Allah is the Most-Just. If we ever perceive any injustice in His religion, it is due to our own lack of understanding, rather than a flaw in the religion.
As you know, men and women were created different in order to complement one another and live in cooperation, and not competition. As with any system, whether in the context of a corporation or a family, each individual is assigned a role based on his or her individual nature and talents.
The vital difference here is that the Lord of the universe is the one assigning the roles based on His perfect knowledge of the nature, strengths, and weaknesses of His own creation.
In His infinite knowledge, Allah has assigned men to be the managers, protectors, maintainers, and providers of the family system. In the Quran, which Muslims believe is the word of God, Allah says what means:
{Men are the protectors and maintainers of women, because Allah has given the one more (strength) than the other, and because they support them from their means} (An-Nisaa 4:34)
However, what many people fail to realize is that with this extra authority comes a great deal of extra responsibility. Men will be held accountable if their families are not protected and provided for.
The Prophet (peace and blessings be upon him) said:
“All of you are responsible and each of you is responsible for his people. The Imam (i.e. ruler) is the guardian of his subjects and is responsible for them. A man is responsible for the people of his house. A woman is responsible for the house of her husband. A servant is the guardian of his master’s belongings and is responsible for them. Each of you is responsible for his people.” (Al-Bukhari)
Part of a man’s protecting his family means protecting their physical needs. Providing food, clothing, and shelter falls under this responsibility. However, his protection is not limited simply to physical protection.
The man must also protect his family’s religion. In the same way he would protect his family if they were struggling to find food, he too must protect them if they are struggling with their religion. If his wife or child is committing unlawful act, protecting them means doing what he can to bring them back into the right path.
You will notice that the reference to 
admonishing the wife is in the same verse, and follows the statement of men being the protectors and maintainers of women.
Allah also says in the Quran what means:
{O you who believe! Save yourselves and your families from Fire…} (Al-Anaam 66:6)
Of course, saving each other from the displeasure of Allah goes both ways. But note that even in a business model, when a manager is not doing his job, the procedure for correcting him is different than the procedure he takes to correct those he manages. Those on the team do not correct the manager directly, but rather take their complaints to his supervisor.
This is done because a manager’s authority over them would make it ineffective to try to address him directly. Instead, they would go to a person who has authority over him. In the case of a family this would mean the imam, an arbitrator (from the family or otherwise), or a judge, for example.
Also, note that when the wife is “misbehaving”, she is to be corrected privately (within the family). When a man is “misbehaving”, he is to be corrected outside of the private sphere (going to an imam, for example). But, this is part of the extra responsibility of taking on a position of power.
In any power structure, those who take on a position of authority must be willing to be censured — sometimes publicly. When the Companion Umar ibn Al-Khattab was Caliph, a woman publicly corrected him by reciting a verse that contradicted what he had said. Omar responded with a smile and said: “The woman is correct and Omar is mistaken.” (Al-Qurtubi, 99)
When a person becomes a manager, with that power, comes the ability to be publicly corrected, if one is not doing one’s job. Consider a college classroom. Who is in the position of authority in this case? The professor is. What happens if a student is loudly talking on their cell phone and disturbing the class? The professor will censure the student directly.
But what happens if it’s the other way around, and the professor is talking on his cell phone rather than teaching the class? Will the students go to him directly? Well, perhaps they might, but that may not accomplish much, if he chooses not to listen. But are the students powerless? No. Most students would recognize that going to the professor’s supervisor would be much more effective.
In the same way, when a husband is not doing his job of protecting his family, whether that means through negligence or mistreatment, the wife should try to advise him. But if he refuses, the wife is told to go to those who can have authority to make him change his behavior. A wife is not powerless. It is quite the contrary.
The system put in place by Allah in fact ensures the rights of the wife. Imagine if a wife was just left to compete with a husband’s extra level of physical strength and authority, and there was no system in place for the wife to go to his “superiors”.
Imagine if those students had no other avenue to change their professor’s behavior besides addressing him directly. Chances are, they would not learn much in the class.
But there is one point, although often overlooked, which is extremely important. Remember that Allah Almighty is always on the side of the oppressed. The Prophet (peace be upon him) said:
“Be afraid, from the curse of the oppressed as there is no screen between his invocation and Allah.” (Al-Bukhari)
So if a wife is being mistreated or oppressed in any way, Allah will be her supporter. Consider the story of the woman at the time of the Prophet who turned to Allah to complain of her husband’s injustice to her. Allah not only heard her calls, He even revealed verses in the Quran to respond to her. Allah says:
{Allah has indeed heard (and accepted) the statement of the woman who pleads with thee concerning her husband and carries her complaint (in prayer) to Allah. And Allah (always) hears the arguments between both sides among you: for Allah hears and sees (all things).} (Al-Mujadilah 58:1)
Allah hears and sees all things. Could there be any greater comfort than that?
I hope this answers your question. Please, keep in touch.
Salam.
Works Cited:
Al-Qurtubi, Muhammad. Al-Jami` li Ahkam Al-Quran. Vol. 5. Riyadh: Dar Alam Al-kutub, 2003.