I feel some sympathy for the wife now that it is clear the husband has left the marriage. His wife is facing an uncertain and possibly bleak future, bringing up two children mainly on her own, although she is wrong to prevent the children from seeing their father, for their sake, not his. At present she feels that the person whom she should be able to rely on for support is twisting the knife still further.
I don't know the reasons why the father left the marriage and it is not my business but he is the one initiating the divorce and I can only assume his wife does not want to divorce. With such young children it is sad that he cannot make more effort to overcome the difficulties, for the sake of the children. It is what all children want, their parents to be together.