Here's your mother and her parents in the 1940 US Census.
"United States Census, 1940," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:KQYX-ZRW : 15 March 2018), Thomas O'Donnell, Assembly District 3, Queens, New York City, Queens, New York, United States; citing enumeration district (ED) 41-630, sheet 3B, line 59, family 96, Sixteenth Census of the United States, 1940, NARA digital publication T627. Records of the Bureau of the Census, 1790 - 2007, RG 29. Washington, D.C.: National Archives and Records Administration, 2012, roll 2733.
John and Lillian's marriage license:
"Florida, County Marriages, 1830-1957," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:FWWQ-2PB : 17 October 2017), John J. O'Donnell and Lillian O. Ashe, 18 Apr 1900; citing Marriage, , Monroe, Florida, United States, Florida State Archives and various county clerks of courts; FHL microfilm 946,974.
Assuming this was her first marriage, at WikiTree we'd write her name as Lillian Octavia (Ashe) O'Donnell.
Oops, her profile is already here, along with her husband and children. And several sources.
No way to tell you anything about your paternal family, because your father's info is privacy-locked.