What is the ruling of Islamic law regarding my divorcing my wife to please my mother, who rejects this marriage due to hearing rumors about my wife, knowing my mother's strong rejection and insistence on divorce; should I obey my mother?

It is not obligatory to obey the mother in divorcing the wife. However, if the husband fears harm might befall his mother if he does not divorce her, then he should divorce her, especially if what was said about the girl is true. If he divorces her before consummation or valid seclusion, she is entitled to half of the dowry stipulated in the contract.