I would ask your mother to help you figure out some other way you can get in touch with your half-siblings if that's what you want, rather than go through your dead father? She might not be as "upset" about your wanting to let your siblings know you exist as about bringing up her past with your father. In any event, I'd discuss things with your mother, being considerate of her feelings though to not discuss your father's and her relationship especially now at this already-trying time of your father's death..