Is the questioner sinful if he limits himself to helping his mother with monthly expenses and saves the rest of his salary for his personal obligations or marriage, given the mother's refusal of the father's guardianship over the sister and the father's deprivation of seeing her?

The mother does not have the right to prevent the father from seeing his daughter. The father's guardianship over his daughter does not cease merely due to his failure to provide financial support, except by court order. His guardianship in marriage is established unless it is forfeited due to the loss of a condition, in which case guardianship transfers to the next in line. The son must explain this to his mother and sister, and remind his sister of her father's right over her. There is no objection to helping the sister financially with her marriage preparations, provided that this does not imply approval of her abandoning her father or marrying without his guardianship. There is no harm in restricting payments to what suffices the mother and saving the rest.