I believe you are correct. I have an old letter written by Lillian [Patten] Ward, wife of Andy M. Ward. Lillian [Patten}Ward was my great-grandmother's sister. In this letter Lillian writes Andrew S. Ward's mother was a Rushing. Also in your last paragraph you mention a William Ward (b. 1844), this was Andrew's brother, William R. Ward, who sometimes went by Robert, and he married as his second wife Lillian's aunt. Her name was Mary Rebecca [Kellogg] Harris. This letter is titled "Ward Family" and is written by daughter in law of Andrew S. Ward so I tend to think this information is correct.