What is the ruling of the Sharia regarding the marriage of a girl to a man who is already married and a father of two children, despite her mother's objection to this marriage?

Obedience to one's mother is obligatory, and showing her kindness and benevolence is commanded by Islamic law. Therefore, you must strive to convince your mother to approve of this man. She should not refuse to marry off someone of good character and religious commitment just because he is already married, for in the Hadith: "If someone whose religious commitment and character you approve of comes to you [seeking marriage], then marry him off." The guardian for marriage is your father, so if he agrees, there is no issue with the validity of the marriage. The remaining issue is that of disobeying your mother's command. We have previously issued fatwas stating that obedience to parents takes precedence over marrying a specific person. However, if the situation is as you described, with you being advanced in age and this man being pleasing in his religious commitment and character, then we hope that there will be no sin against Allah nor disobedience to your mother in this matter, while striving to show her kindness and appease her.