All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If a wife leaves her husband's home without his permission, then she is disobedient to him, and Allaah explained to us the steps that a husband should take in dealing with a disobedient wife and this is discussed in Fatwa 89480.
So if your wife left your home without your permission and without a sound Islamic excuse, then she is a disobedient wife.
However, you should not have hit her before exhausting the other steps that come before hitting when dealing with a disobedient wife. If you hit her severely then you were wrong and if she left your home in order to repel the harm from her, she is not sinful for leaving the house without your permission.
The fact that she is arguing too much is dispraised in Islam because it is an obligation on the wife to obey her husband as long as he does not order her to disobey Allaah. However, you can solve the problem of her arguing too much with admonition and advice. If this is without any avail, then you can hit her without leaving any scars or marks provided that hitting does not lead to a greater harm than the benefit that is expected from hitting her, for instance if hitting her leads her to becoming more disobedient or leaving the home as it happened.
In any case, we advise you to continue endeavouring to reconcile with her as reconciliation is good especially that Allaah blessed you with children with her.
First, we advise you to seek Allaah's Help, then the help of whomever you think could influence this woman and her family so that they would remind her that it is not permissible for her to refuse to go back to her husband's home, and remind her family that it is not permissible for them to prevent her from going back to her husband's home. If reconciliation takes place, all perfect praise be to Allaah. However, in case they refuse, you should take the case to an Islamic centre to look into the matter and take the appropriate solutions.
Allaah Knows best.