How should one deal with a husband who feigned piety and claimed to have divorced his first wife in order to marry, then it was discovered that he is still married to another?

If the husband is just between his two wives in terms of lodging and sustenance, and he is committed to the obligatory duties, then it is advised to remain with him. Requesting a divorce from him without a legitimate Shar'i reason is an act of disobedience. It is not permissible for a wife to ask her husband to divorce her co-wife, and his lie about divorcing his wife is a sin upon him.