The only family relationship that I have found for theAddington family and the Bitts family is in the 1880 census data:
1880 Census:Fort Russell, Madison Co., Illinois, pg 230C Jeremiah Bitts, 60, b. 1820, PA/PA/PA(widowed) Eliza, Bitts, 32, dau, b. 1848, MO/PA/Eng Wm Bitts, 36, son, b. 1844, PA/MO/Eng Dorothy Addington, 85, Mother in Law, b. 1795, Eng
Your dates do not agree with the census dates so could they be wrong.This Dorothy Addington and her husband William Addington appear in the 1850 census in St. Louis, MO.They had a daughter, Ann Addington, b. 1822, who married a Jeremiah Bates according to one source.
For more information on this family, see the Addington Immigrants (#7) at the Addington Association website (http://www.association.addington.com).There is also a short descendants list (St. Louis Addingtons) for this family at the webpage: (http://www.association.addington.com/marylandaddingtons.htm)