In case you haven't come across it before "A Village of Considerable Extent" (South Normanton) by Pamela Sharpe has
"Illegitimacy seems to rise with poverty from 1795 and the unmarried mothers who claimed relief at this time belonged to families whose names recur in poor relief documents"- Ball, Hind, Kite, Marriott, Bacon, Hill. Many were sisters or "repeaters" who had two or more illegitimate children.
Illegitimacy was a constant bugbear to the Overseers of the Poor. When Jane Ball was delivered of a male child on the ninth of January 1809 Thomas Moaks of South Normanton did beget the said bastard child in the body of her and was ordered to pay £1 8s 6d maintenance plus 18d weekly for the keeping and sustenance of the child. Jane Ball was to pay 9d weekly in case she did not look after the child herself. By 1812, however, Thomas Moaks was behind in payments to the sum of £3 15s 0d."
I have Mary Gent, a repeater, in my tree. I found details of the two different men who fathered her daughters in the SN Quarter Sessions records. If you haven't done this, worth a look for Samuel.
My best guess is that Samuel Kyte is the son of John Shawcross and Jane Ball and was bpt as Samuel Ball or not at all and subsequently assumed the name Kyte, although, as you say, the birth date of circa 1820 is odd given the birth of Abraham and Isaac in 1817. When and where did John Kyte and Jane Ball marry?
Valerie