How does Islam judge a wife who -after she left her husband without divorce and left her children for him to raise - tries to make the children hate their father although the father is a very good Muslim and loves his children? She also married another man without getting divorce.

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

If the situation is as you described, then this woman who left her husband without divorce and married another man has committed a grave major sin and deserves the most severe punishment that dissuade her and any other woman who might be dragged by Satan to go beyond the limits of Allah and commit such a dreadful act. Now, if it is possible to bring her case to an authority that can separate her and the man who is committing Zina (fornication or adultery) with her and prevent her from going beyond the limits set by Allah, then this should be done immediately. On the other hand, the fact that this woman tries to sow hatred in the minds of these children against their father is yet another obnoxious act which aims at breaking kinship ties. Indeed Allah curses anyone who tries to break kinship ties. Allah Says (what means): {So would you perhaps, if you turned away, cause corruption on earth and sever your [ties of] relationship? Those [who do so] are the ones that Allah has cursed, so He deafened them and blinded their vision.} [Quran 47: 22-23]

This woman has committed three different major sins starting by her deserting her husband's home, then committing Zina (adultery), and finally endeavoring to break family kinship. She must beware of Allah's Punishment. Allah Says (what means):

• {And whoever disobeys Allah and His Messenger and transgresses His limits - He will put him into the Fire to abide eternally therein, and he will have a humiliating punishment.} [Quran4: 14]

• {So let those beware who dissent from the Prophet's order, lest fitnah strike them or a painful punishment.} [Quran 24: 63]

Therefore, this woman must repent before it becomes impossible for her to do so as death can surprise a person at anytime. Allah Says (what means): {Say, “O My servants who have transgressed against themselves [by sinning], do not despair of the mercy of Allah. Indeed, Allah forgives all sins. Indeed, it is He who is the Forgiving, the Merciful.” And return [in repentance] to your Lord and submit to Him before the punishment comes upon you; then you will not be helped.} [Quran 39: 53-54]

Allah knows best.