How can a young man reconcile his desire and need for marriage with the care of his mother, who refuses his marriage and will not accept living with him, in order to avoid falling into sin or disobedience to his mother?

Filial piety towards one's mother is obligatory, especially during her weakness and illness. However, this does not preclude the necessity of marriage when there is a fear of falling into sin. You must take the initiative to marry, and you are not obliged to obey your mother if she prevents you from marrying when you fear falling into sin. After marriage, continue to be dutiful towards your mother by serving and caring for her, and try to appease her. Know that taqwa (piety) towards Allah and reliance upon Him are sufficient for you.