Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
If there is no valid excuse for the husband`s behaving in the above manner, then it isn`t lawful for him not to greet his wife with the greeting of Islam and turning his house into a place of conflict, hatred and bile. Rather, he should realize that solving family problems starts with dialogue and understanding, in addition to turning to Allah in supplication and abiding by His commands. Moreover, the children shouldn`t be the victim of this conflict since their upbringing is a shared responsibility. The evidence on this is that Ibn 'Umar (May Allah be pleased with them) reported: The Prophet (PBUh) said: "All of you are guardians and are responsible for your subjects. The ruler is a guardian of his subjects, the man is a guardian of his family, the woman is a guardian and is responsible for her husband's house and his offspring; and so all of you are guardians and are responsible for your subjects." [Al-Bukhari and Muslim].
The wife should sit with herself, try to find out the reason for his avoiding her, and try to fix it, even by waiving some of her personal rights for the sake of the children and maintaining family ties. This is attested to in the following Hadith: Abu Hurairah (May Allah be pleased with him) reported: Messenger of Allah (PBUH) said: "Wealth is not diminished by giving (in charity). Allah Augments the honour of one who forgives; and one who displays humbleness towards another seeking the pleasure of Allah, Allah exalts him in ranks." [Muslim]. And Allah The Almighty Knows Best.