What was the mistake made by the questioner, and what advice is directed to him, given that the girl's family refused to complete the marriage and blackmailed him after disclosing her illness, especially since the matter has already concluded?

We do not know whether the reason for accepting the divorce is permissible or not. However, if the wife requests a divorce without a valid reason, the husband has the right to refuse until she waives some or all of her rights. They should have informed you of her illness that prevents conception. As for the dispute over the Mahr (dowry), its reference is the Sharia (definition) court.