There was a Gladys S Ellis born in 1913, parents Frank Ellis and Ellen Smith...https://familysearch.org/pal:/MM9.1.1/FXVN-V6K
Also recorded as mother name of Nellie, with no surname...https://familysearch.org/pal:/MM9.3.1/TH-266-12344-207997-78...
Same date of birth. The Ellen Smith record was registered June 12, 1913. The Nellie record was registered Jan 3, 1914.
Frank and Annie had a son Frank Jr. I assume he is the father of Gladys.
His WWI draft card lists him as married with 2 children.https://familysearch.org/pal:/MM9.1.1/KZN3-1GJ
Here is a possible fit for him in 1920, on Cedar St but at a different address. Caroline was likely a Wilcox as his in-laws are living with them.
1920 United States Federal Census about Frank Ellis
Name: Frank Ellis
Birth Year: abt 1894
Home in 1920: New Bedford Ward 3, Bristol, Massachusetts
Relation to Head of House: Head
Marital Status: Married
Spouse's Name: Caroline Ellis
Father's Birthplace: Massachusetts
Mother's Birthplace: Massachusetts
Home Owned: Own
Able to Read: Yes
Able to Write: Yes
Neighbors: View others on page
Frank Ellis 26
Caroline Ellis 23
Eleanor Ellis 3 3/12
Albert Wilcox 48
Mary Wilcox 46
It's possible that Gladys was born out of wedlock, and was really Frank and Annie's grandchild, but recorded as Niece. Purely speculation on my part.