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, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.
There is no doubt that your wife's disobedience to you in what is permissible is unbecoming of a Muslim wife, and by so doing she is being disobedient to Allaah and she violates your rights as a husband. In fact, this is considered Nushooz (recalcitrance against her husband), and you should treat it according to the instructions of the Islamic law in dealing with the recalcitrant wife as explained in Fatwa 85402.
Indeed, lying is an evil trait, which is not from the nature of a believer. The fact that your wife claims that she was predetermined to be a liar is another prohibited act that adds to her sin of lying. She is following the example of the disbelievers about whom Allaah says (what means): {Those who associated with Allaah will say, "If Allaah had willed, we would not have associated [anything] and neither would our fathers, nor would we have prohibited anything." Likewise did those before deny until they tasted Our punishment.} [Quran 6:148] Verily, if such an excuse was of any good, it would have benefited those disbelievers and polytheists.
It should be noted that the religious concession granted to the spouses to lie to one another is confined to cases when it is expected to lead to good valid ends such as increasing the love and affection between them.
In any case, praying for her is one of the most important means to rectify your affairs, in addition to saying good words, for they have a positive effect on the person, especially women given their emotional nature. Similarly, presents have a good effect on the heart. The Prophet, sallallaahu ‘alayhi wa sallam, said: "Give presents to each other and you will love each other." [Ahmad and At-Tirmithi - Al-Albaani graded it Hasan (good)]
Finally, exposing children to the fights between their parents is a serious issue. It is important for parents to keep their conflicts behind closed doors and away from their children. Therefore, remind your wife that the least that can be done in this regard is to keep your disputes and conflicts away from the children and that they only see mutual love and respect between you. We would like to remind you of seeking the help and mediation of wise relatives from her family if necessary.
Allaah Knows best.