It looks like you have done some pretty good research. You are probably correct that they are two entirely different Jesse Slaughters born within the same decade.
I found a son of the "other" Jesse, Slaughter(-14) . The son is named Simon and was born in 1817. Unfortunately he still could possibly be the son of a second wife (Mary Rollins) of your Jesse, if there actually is a second wife. I was hoping the date would prove it impossible.
"West Virginia Deaths, 1804-1999," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:N9ZG-WVK : 4 December 2014), Jessie Slaughter in entry for Silas H. Slaughter, Sep 1906; citing Belgrove, Jackson, West Virginia, County Records, p 48, county courthouses, West Virginia; FHL microfilm 567,216.
Name Silas H. Slaughter
Event Date Sep 1906
Event Place Belgrove, Jackson, West Virginia
Age (Expanded) 89 years
Birth Date 1817
Father's Name Jessie Slaughter
Mother's Name Mary
I also found a query on a genealogy forum from 2007 with several posts that you might find interesting if you haven't already discovered this:
There is a discussion about the two possible Jesses. I was going to cut and paste some of it, but there is too much, so I won't try to figure out what would interest you.
You may need to try to contact the profile manager of Slaughter-14 , just to make sure there isn't additional information to untangle, and to ensure there wouldn't be any hard feelings if you disconnect the other Jesse from Robert, but it looks to me like that manager may not be active. I feel that your instincts are correct, and there shouldn't be two sons named Jesse -- but I didn't really find anything conclusive that they weren't the same person (and I didn't continue to try to follow the paper trail.) I personally feel that unless you can find evidence that they ARE the same person, that Slaughter-14 should be disconnected from Robert to make it more likely that the real facts will be located. I hope someone else chimes in if I'm steering you wrong, though.