What is the Sharʿī ruling regarding the marriage of a religious girl to a religious young man whose religiosity and character she is pleased with, while the mother rejects this marriage because he is not from the same family, considering the girl's fear of displeasing Allah if she pleases her mother, or displeasing her mother if she pleases Allah?

Obeying your mother is obligatory, and you must strive to convince her to marry you to the suitor. However, if she insists on refusing without a legitimate Sharia-compliant reason, and the suitor is pleasing in his religion and character, then there is no sin upon you in accepting to marry him, and this is not an act of disobedience. What is considered in compatibility is religion and character, and the guardianship of marriage (wilayat al-nikah) belongs to men, not women.