Can the case filed by the wife's father be won despite the existence of documents proving the wife's previous pregnancy, and what is the ruling of Sharia on the husband's desire to divorce his wife when he is unable to pay her legitimate dues?

A definitive ruling on the matter cannot be made due to a lack of complete knowledge of its circumstances. However, if intercourse occurred, this refutes the claim of impotence. The husband has the right to request a khulʿ (divorce at the wife's instance, usually with compensation) from his wife if she seeks separation without a legitimate شرعي justification. It is not permissible for a woman to seek divorce without a legitimate شرعي reason, nor to resort to deception by fabricating false accusations against the husband to dissolve the marriage without khulʿ. This constitutes an attempt to cause separation between spouses and an infringement upon a Muslim's right, both of which are forbidden.