To what extent is the husband's supplication permissible: "O Allah, by Your knowledge of the unseen, if there is no good for me in her [i.e., the wife], then relieve me of her," and is repentance and seeking forgiveness sufficient if the supplication was misguided?

What the husband prayed for does not contain any Sharia violation unless he intended to be rid of her through her death, in which case it would be a violation of the Prophet's prohibition against praying against oneself, one's children, or one's wealth. It is preferable that he prays for her guidance and righteousness.