Let me work on this a bit as there are a fair number of Rider/Ryder's from KY in the area and time of concern. Here is Houts Rider Family
1850
George Rider
Age: 49
Birth Year: abt 1801
Birthplace: Kentucky
Home in 1850: Blue, Jackson, Missouri
Gender: Male
Family Number: 758
Household Members:
Name Age
George Rider 49
Ailsey Rider 44
Eliz A Rider 21
Mila Rider 19
Samuel Rider 16
Mary Rider 14
John Rider 12
Oliver Rider 10
Elizabeth Rider 7
1860
Name: George Rider
Age in 1860: 53
Birth Year: abt 1807
Birthplace: Kentucky
Home in 1860: Sni a bar, Jackson, Missouri
Gender: Male
Post Office: Stony Point
Value of real estate: View image
Household Members:
Name Age
George Rider 53
Alicy Rider 54
Miley Rider 27
Oliver Rider 21
Elizabeth Rider 16
Here is your George Ryder in Saline Co :
1850
George Ryder
Age: 47
Birth Year: abt 1803
Birthplace: Virginia
Home in 1850: District 90, Saline, Missouri
Gender: Male
Family Number: 218
Household Members:
Name Age
George Ryder 47
Anna E Ryder 35
Thomas Ryder 21
Nancy Ryder 17
John Ryder 15
James Ryder 13
Margaret A Ryder 11
Lucinda Ryder 10
Minerva Ryder 6
G Marshall Ryder 5
Mary Ryder 2
1860
Geo Rider
Age in 1860: 50
Birth Year: abt 1810
Birthplace: Virginia
Home in 1860: Miami, Saline, Missouri
Gender: Male
Post Office: Marshall
Value of real estate: View image
Household Members:
Name Age
Geo Rider 50
Ann E Rider 50
Lucinda Rider 17
Manerva Rider 15
George M Rider 14
Mary L Rider 12
William Rider 7
Margaret Rider 5
As you see there is not a Mart or Martin Ryder/Rider noted unless Mart is a nickname for George Marshall Ryder of Saline Co, however in the 1860 census in Vernon County we find this Martin Rider with wife Alsy native of TN which fits Mr Wood's findings excepting the family tie to James Ryder (Saline Co)
Name: Martain Rider
Age in 1860: 26
Birth Year: abt 1834
Birthplace: Tennessee
Home in 1860: Little Osage, Vernon, Missouri
Gender: Male
Post Office: Little Osage
Value of real estate: View image
Household Members:
Name Age
Martain Rider 26
Alsy Rider 26
Granvil C Rider 5
Alford Rider 4
J W Rider 3
Sarah A Rider 2
Nancy Thompson 4
Heie?? Cummins 23
Martin J Ryder has a CSR that lists him as a 1st Lt, Co. C, Jean's Regt 12 MO Cav, Commissioned Jackson Co. MO 12th Sept 1862, by Col Thompson, enlisted 12 August 1862 Jackson Co, Native of Sumner Co, TN. He is listed on a return of that company Feb 1863 as absent on leave of absence since Feb 8th 1863.
In the PM files of US vs George Ryder of Saline Co prosecuted by the PM at Marshall MO. Several affidavits report conversations with Ryder that his son James was a bushwacker and operating in the area Oct 1862 through May or so of 1863.
Furthermore there is return of Quantrell's company that includes a George Rider and J.M Rider that fits the ages of the Jackson Co Rider clan. Further there is an entry for a George and John Rider both in Co D Musser's Batt. MO Infantry both listed as deserters Jan 11 1863. Enlistment is listed as August 1862 at Clinton MO.
Talitha Alice Rider's PM file has a statement she was married to "Jim Rider" (quotes in statement) as early as 1857 and "Jim Rider" was harbored by his Uncle George in Saline County. I've no problems with this as several affidavits list her and her husband as longtime residents of Livingston Co. In fact there is a draft record for James Rider 1863 Livingston Co Missouri listed as 28 years old (born abt 1835) native of Vermont who failed to report in Dec 1863. This fellow appears to show up in Ismerelda Nevada in 1870. So I'm not totally convinced that Talitha was actually married to James Ryder of Saline Co at this stage given the apparent proclivity of the Union officials to always put "Jim Rider" and "bushwacker" in quotes leads me to believe they were not sure of the connection as well. FWIW
Therefore I think I've got to say that if any of these 4 clan's (Saline/Virginia, Jackson/Kentucky, Vernon/Tennessee, Livingston/Vermont) are related it happened at least 2 generations prior to them being in Missouri.
I'll chart and structure this sometime over the next few days...
John R