Is a wife considered sinful if she secretly prays to God to compensate her with a righteous husband in this world, given her mentally ill husband's neglect and severe shortcomings in fulfilling her rights?

A woman should be patient with her husband and advise him, and frequently supplicate for his rectification. If living with him becomes impossible and she is clearly harmed, then she has the right to seek a divorce, and there is no sin in supplicating for it at that point.