Here are some other thoughts on how to deal with the criticism. Have you ever heard of the Eggerichs' book on Love and Respect? You could read that with your wife or try to find a church that has a Bible study program. It is really good for your situation. It explains how sometimes when women think they are helping or sharing their thoughts, the man takes it as disrespect. It would be good for your wife to see that, and to hear it from someone else. Sometimes hearing it from an expert helps convince someone.
If she's being hypercritical, don't take it to heart. If she yells or calls names, you can also disengage and say you are willing to talk when she is able to have a conversation calmly like an adult.
You need to hold her accountable about respect and submission. Some people say men shouldn't worry about that, that it is all on the woman. But the man is the head of the woman, and as a husband you want your house run well. You could also say it is up to the children to decide whether to obey the parents, but that would be a lousy method of running a home. Preachers apply servants obey your masters to the workplace and employment situations. Imagine a manager who let his employees decide to follow company policies and his own instructions without doing anything if they chose not to?
You need to create a situation which makes it easier for your wife to obey Christ. One aspect of obeying Christ is submitting to you and respecting you. Leviticus says to love your neighbor, not to despise your neighbor in your heart, but rebuke your neighbor frankly so that you do not share in his sin. This isn't really a part of American Christian culture very much, but the New Testament is full of instructions for believers to exhort and admonish one another. Jesus says that if your brother sins against you to tell him his fault between you and him alone (the firsts step.) As a believer, you are required to offer some correction if a fellow believer sins against you. That definitely applies to the husband and wife relationship. And as the husband, you have a household management responsibility and your wife is included in that. And you are the head of the wife.
I shouldn't have had to argue the case, but yes you do need to offer your wife some accountability on the respect issue. If she is a fellow believer, at least theoretically, you will have some common ground. I realize in today's day, there are plenty of people who call themselves Christian who will try to talk a woman out of the idea that she has to submit to or respect her husband. They'll jump to the most extreme case ("you don't have to obey him if he tells you to shoot children") or try to redefine the Greek words translated submission or respect/reverence. But hopefully, you can find common ground.
One thing to do, if you are both believers or if you are and she's okay with it, is to study the Bible regularly and pray with her. You can read through other books like Love and Respect, which may really help your marriage, in addition to Bible study. Certain passages will give you an opportunity to address marriage problems.
Let her know that you expect to be respected. It is your duty as a husband to hold her accountable on this issue just as you would if she were to go out and get drunk and drive home. Hopefully, you would admonish her if she did something like that. Well, if she isn't submissive and respectful to you, she's not being submissive and respectful to the Lord. She is to submit to you as unto the Lord. And if she is sinning in that area, it is actually against the Lord. The children of Israel complained about the manna after they ate it for a while. But they were actually complaining against the Lord, since that was the provision the Lord gave. You are the provision for your wife as a husband.
Hopefully, you can get her to 'buy in' on the idea that she needs to be respectful. Hopefully you can have a conversation where you point out some way in which she was disrespectful to you and she knows that is wrong. Let her know the types of behaviors you consider to be disrespectful, the types of things she says to your family, ignoring you while you are talking to her (in private, but especially in public), saying insulting words.
You also have to lead by example about insults of course. Jesus said that the one who called his brother Raca (translated 'worthless' by some) would be in danger of the council and the one who said 'thou fool' would be in danger of Hell fire. So saying angry insulting words is a serious thing for the Lord. So you have to both agree never to call the other stupid or dirty words. Fortunately, my wife and I have kept from that throughout our marriage.
Then your wife needs to know what kind of things are inappropriate for her to say about you around her family, jokes, insults, or whatever. She needs to respect you, and she need to do it in a way you consider respectful, not according to her own standard. If she disagrees with that concept, you could point out that she is also to submit to you, and as a matter of submission you ask her to treat you with a certain standard of respect.
Sometimes a submission, respect, etc. discussion goes nowhere. She refuses to talk, gets emotional, etc. You can still try when she's in a better mood. But if you reach an impasse, you can go to prayer and pray through the hardness and ask the Lord to go to work on her heart. The Love and Respect book may help if she won't listen to you. She may listen to others.