I will give you my theory and also one more small bit of information.
My theory is that Lillie Mae Connor (or Conner) married George Adolph, Sr. in 1883.They then had 3 sons:Alfred, Ellwood, and George, jr. (your father).(I have no idea whether they actually used "sr." and "jr." but these labels help keep things straight for now.)Geroge Adolph, Sr., then either dies or leaves the family.All of this has been taking place in New Jersey.Then, in 1900, Lillie Mae Adolph is living with her three sons AND my greatgrandfather William J. Sherwood (or William I. Sherwood) as a lodger.In 1906, Lilly and William Sherwood marry and she becomes Lilly (or Lillie) Sherwood.In 1910, in Manhattan, they are still living with the 3 sons of Lillie and George, Sr., Adolph.The three sons are in their twenties.The census does not give them a last name, but I think they never became adopted as Sherwoods.In any case, George, Jr., your father, retains the name Adolph, has does his brother Ellwood, who subsequently appears in the 1920 and 1930 Federal Census with the last name Adolph and a wife, Bessie M.There is no evidence that they had children, unless it was after 1930.I haven't been able to find your father George Adolph in either the 1920 or 1930 census--well, at least not yet.
Now, as for why your picture is labeled "George and Lillie Mae Sherwood".Let me ask:From the picture would you say this is your dad, George?Or your grandfather (George, Sr.)?In any case, I think your mom might have assumed there would be no confusion (since your name was Adolph) and that "George and Lillie Mae Sherwood" means "George Adolph and Lillie Mae Sherwood".That is, your grandmother was then known to your mom by her second married name, Lillie Mae Sherwood, because her first husband had been dead many years and thus your mom was likely to know her mother in law as Lillie Mae Sherwood.By the way, my middle name is Sherwood, so it is fun to do this research.My father was 20 years older than my mother...so I was born in 1948 and there wasn't much living memory of these folks by the time I came along.
As for my little bit of new information:I find a William J or I Sherwood living with his wife Lilly Sherwood in Philadelphia, PA, in the 1920 federal census.I am pretty sure that this is our relatives--but there are no children (Ellwood, Alfred, Geroge) with them and Lillie doesn't have her middle name, so it is hard to be sure.On the other hand, the ages are correct for the two of them.William did have a daughter living in Philadelphia at the time (my grandmother, Emily), so I am pretty sure that we have now followed William and Lilly in the 1900, 1910, and 1920 census.We had Lilly with her parents in the 1880 census (just before she married the first time to Georege Adolph in 1883).The 1890 census burned up in a fire, so we are missing that step.William was to die in 1924 (I believe from a cryptic hardwritten note I found).I am not sure when your grandmother Lillie died but please let me know if you find that--or where she is buried.Perhaps my greatgrandfather William and she are buried together.
Anyway, it is a pleasure to hear of your picture.Perhaps if you sent me an email note, I could send you my mailing address?