Is the father's ex-wife considered a kinship relation, and is there a sin for not seeing her, and what are her rights over her former husband's children?

The woman mentioned is not considered a relative by virtue of your father marrying her, unless you are related to her through your father or mother's side. In that case, she would be considered a relative; otherwise, not. You should treat her kindly and with beneficence because she was one of your father's beloved, in accordance with the Prophet's (peace and blessings be upon him) saying: "The best of righteousness is for a man to maintain ties with the loved ones of his father after he has passed away."