Faith, I have been looking at the 1840 census for Jesse Been on Ancestry.com and came up with two of them one in Calloway County which is the one you wrote down in your message but he doesn't fit the age for the Jesse in 1850 Van Buren County even though he did have neighbors that was Kaylors but the other Jesse was in Graves County and his age and his wife age fits for the ones in Van Buren County and so does the children but there are some that are older females and one male that doesn't show up in 1850 census.
Here is the Graves County 1840 Jesse compared to the 1850 census Jesse of Van Buren County 1850 census age in Parenthesis
Jesse Bean 1 male 40-50 (Jesse 58) 1 male 5-10( unknown) 1 male 0-5 (George 13) 1 female 30-40 (Lucy 48) 1 female 15-20 (unknown) 1 female 10-15 (unknown) 1 female 5-10 (Katherine C. 17) 2 females 0-5 (Permeliann 15 and Lydia J. 11).
I will agree with you that P. Hartwick is Polly C. in the 1860 census and by 1870 she could possibly be married since they at times marry at 14-16 years old during those times or may have died before 1870.