The family in 1939 at Swan Cottages appear to be related to the marriage in 1905:
Henry Stone and Rose (Annie?) nee Maxted
but something seems to have happened to the relationship as in 1921 Rose and some of her kids as listed as Wood with Albert E Wood who she married (bigamously?) in 1917.
In 1921 Henry Stone is indexed as "Shone" with a number of children to "Maud" (in 1939 Alice M - no marriage to be located as far as I can see).
This includes a Florence, 1910, and an Agnes, born 1913, who might be Maud's daughters from a previous relationship, and later children who also are listed with mother's maiden name MAXTED.
Now:
Florence Daisy Rose, born 1910, mother's maiden name MAXTED
Agnes Rose, born 1913, mother's maiden name MAXTED
I cannot find a Rose/Maxted marriage, or a later Rose/Stone marriage, but I can find an Alice Maud Maxted born 1885 Dover.
So, in summary:
Agnes may have been born Agnes Rose to Alice Maud nee Maxted, Henry Stone was either her biological father, or a stepfather, but either way from a young age she likely used the name Stone and indeed may not have known her birthname.
I suggest you look again at the DNA connections to see if you have Maxted or Rose popping up.