I have a record for a John Rule married to Elizabeth Kent on 4 March, 1849 in Morgan County, Indiana. I believe this John's father is George Rule (born ABT 1800 Tennessee).This John, that married Elizabeth Kent, is the brother, I believe, to my 4x great grandmother Celia Rule. I don't have Harriet listed as one of their children. I have them listed as: Thomas J. Rule b.1852 Silas Rule b. 1854 Rebecca Rule b. 1855 Sarah F. Rule b. 1858 Jonathan W. Rule b. 1862 The dates for Harriet that you gave don't jive with the dates of his other children. I also don't see that John who maried Elizabeth Kent would have been married to an Emily at the time of Harriet's birth.
I believe the John Kent who married Elizabeth Whitaker (October 22 1863 in Morgan County, Indiana) is the John that is the son of James Rule and Catherine Hood.
I have Harriett Angelina Rule marrying Emanuel Koons on May 17 1870 in Morgan County, Indiana.
Sorry if this didn't help much, just thought I would contribute a few thoughts.