Wife is blackmailing and abusive. How to protect myself and children?

Legally you cannot do anything apart from giving a Divorce to your wife.

We suggest that you should see a marriage counselor to settle the dispute or else the other option available to you will be to file a petition for divorce on the ground of cruelty in the competent court.

Under Section 13(1)(ia) of the Hindu Marriage Act, the term cruelty includes mental as well as physical cruelty. Mental cruelty has been elaborated upon by the Supreme Court of India to include:

“Mental cruelty may consist of verbal abuses and insults by using filthy and abusive language leading to constant disturbance of mental peace of the other party. The Court dealing with the petition for divorce on the ground of cruelty has to bear in mind that the problems before it are those of human beings and the psychological changes in a spouse's conduct have to be borne in mind before disposing of the petition for divorce. However, insignificant or trifling, such conduct may cause pain in the mind of another. But before the conduct can be called cruelty, it must touch a certain pitch of severity. It is for the Court to weigh the gravity. It has to be seen whether the conduct was such that no reasonable person would tolerate it. It has to be considered whether the complainant should be called upon to endure as a part of normal human life. Every matrimonial conduct, which may cause annoyance to the other, may not amount to cruelty. Mere trivial irritations, quarrels between spouses, which happen in day-to-day married life, may also not amount to cruelty. Cruelty in matrimonial life may be of unfounded variety, which can be subtle or brutal. It may be words, gestures or by mere silence, violent or non-violent.”

Thereby, the behavior and the abusive language of your wife can come under the ambit of Cruelty as a ground for Divorce.