Is it permissible for the wife to use government insurance that her husband obtained through false information, knowing that, and what should she do about it?

The questioner bears no sin if her husband is angered by her seeking what is lawful and avoiding what is unlawful, for obedience to Allah takes precedence over obedience to anyone else. This is based on the Prophet's (peace be upon him) saying: "There is no obedience to a creature in disobedience to the Creator," and "Verily, obedience is only in what is good and right."