1.  Jordan R. Dodd, ed.  1993.  Kentucky Marriages:  Early to 1850.  Liahona Research, Orem, UT (Broderbund CD-229):

Tyler, Marcus M.

Mims, Sarah Jane

May 25, 1842

Caldwell Co.

2.  1850 Census Index/Microfilm (online at GenealogyLibrary.com):  1st District, Trigg Co., KY, p. 290B, 13/13, enumerated 2 Aug 1850 (extracted by Diana Gale Matthiesen):

M M Tyler	35	M	Lawyer		Virginia
Sarah J Tyler	31	F			Kentucky
R H Cobb	14	M			same
Irene Cobb	13	F			same
Linah M Cobb	12	M			same
Byron O Mims	11	M			same
John H Mims	9	M			same
Linah Mims	7	M			same

It's a little hard to say exactly who the children are, though all would seem to be Sarah's nieces or nephews.
 
 

Sarah's sister, Julia (MIMS) COBB, wife of Dr. Joshua COBB, died in 1841.   She had son, Robert, born 1840, and a daughter, Irene, born 1838, but they are living with their father and step-mother in the 1850 census of Stewart Co., TN.  The latter census was not enumerated until December, so it may be the children were accidentally enumerated twice, with an error in Robert's age, but it's a stretch and it doesn't account for Linah M. 

The MIMS children are said by some sources to be sons of Sarah's late brother, Col. John Harrison MIMS, and his wife, Caroline Hanson CRESAP, but this seems doubtful.  Although Col. John died early in 1850, his wife is said not to have died until 1909, so why would her children be living with her sister-in-law in 1850?  I have yet to find widow Caroline or any of her (other) children in the 1850 census, so I suppose it's possible she and her children were scattered after Col. John's death.  But this scenario seems unlikely as the Col. was obviously a man of means, so Caroline should not have been destitute, which is the only reason I can think of for the family being split up.  Unless, of course, Caroline went off the deep end over Col. John's death or remarried almost immediately, with the step-father rejecting the children or they rejecting him, preferring to live with their aunt.  Surely Col. John, as a man of means, left a will, which would at least identify his children.  We may have our answer in that other secondary sources say Col. John's only son was Hanson MIMS. 

Sarah has two sisters and a brother whose spouses and children have not been identified.  So, for now, I'm leaving the parentage of these children an open question, though I think there is little doubt they are the grandchildren of Col. Linah & Rebecca (__?__) MIMS.