I suspect that this is your Frank at age 2, erroneously enumerated as a daughter.
1940 Athol, Worcester, MA Hart, Francis J. 25 ME Eunice L. 26 MA Francis J. 2 dau NY Patricia A. 1 dau MA Tole, Jane E 65 VT grandmother
If I am correct this is Francis J. Hart (b. 1915) 1920 Ludlow, Windsor, VT Tole, Michael 62 VT Jennie 44 VT (nee Mcginnis/McGuiness) Hart, Mary 22 NH, (md to Frank Hart)Mary b. 8/19/1897 d. 8/21/1924 Hinsdale, NH of TB Tole, Ruth 19 NH Hart, Francis 5 MEMA NH grandson Hart, Minnie 3 VT MA NH granddaughter b. 3/12/16 Hart, Rodger 1 VT MA NH grandson b. 3/13/1918 d. 5/1978 Worcester, MA (In 1935 they say they lived in NY)
Mary Elizabeth Tole md Francis Joseph Hart 7/20/1914 Ludlow, VT.
WWI Draft Ludlow VT 6/5/1917 Francis Joseph Hart b. 4/7/1895 Lawrence Mass (SSDI & birth record have April 8) occ:spinner-Black River Woolen Mill Ludow, VT married- supports wife & 2 children Tall, Stout, Blue eyes, Black hair
After Mary's death, it appears that their children were sent to an orphanage in Hampden Co. MA.(Roger at Holy Family Brightside Orphanage, Frank living as boarder with unrelated family.)Frank remarried to an Irene, and had two more children: Robert L. b. 2/16/1927 and Norman F b.12/1/1929.
Here is Frank Sr. with his parents 1900 Lawrence, Essex, MA Hart, Joseph 33 Dec'66 MA IRE IRE , married 12 yrs Margaret 30b. 1870 Ire mother of 6, 3 living Joseph 10Feb'89 MA Thomas 7 Oct'92 MA Francis M. 5 Apr'95 MA
In 1910 this family is living in Madison, Somerset, ME and has added a daughter Margaret b. 8/31/1902 Lawrence, MA.
Michael R. Tole age 40 married Jennie McGuiness age 22 on 11/28/1895 in Keene, Cheshire, NH His F: Harry Tole His M: Mary Glass Her F: Nathan McGuiness Her M: Kate McEnleer
Jennie Tole lives in Athol 1946-1952 directories
If this is all correct, Your Frank J. Hart who had a child with Donna Bates was likely Francis Joseph Hart III.