Hi,I dont know if you have this or not but I found Rose and Julio in the 1920 census in Britol County, New Bedforn Ward 3.

Encarnaceo, Julius/age27/ImmigrationYear1910/ALLBornCapeVerde/Fireman
Rose L. Wife/age30/ImmigrationYear1901/ALLBornCapeverde
Cassemiro Son age 12 born Mass.
Annie Dau age 3 born Mass.
Mary Dau age looks like 6 months born Mass

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Now in 1910, I found her in Bristol Co. New Bedford Ward 5

Rose, Manuel/age23/Married 4 years/Born Atlantic Islands/Cotton Mill
Rose, Rose/age20/Married 4 years/Born Atlantic Islands/Cotton Mill
Rose, Cazemeria(spelled that way in the census) age 3 born Mass

Now here is what is interesting. Rose, Manuel and there son, Cassemiro are listed as borders. They are living with Manuel Fayal and Mary Fayal.

Fayal,Manuel Head/age35/bornAtlantic Isl./Married 6 years/No Children
Fayal,Mary Wife/age 35/born Atlantic Isl/ No children

So, it would appear to me that Manuel and Mary Fayal could not be Rose's parents because the census record indicates in 1910 that they had no children and that they only been married 6 Years. However, since Mary Fayal is 35 and Rose is 20, she could have had Rose at 15 in Cape Verde

Also, 1910 maybe Rose's first appearance in the Cenus since it appears that she arrived in America after 1900.

I hopes this helps.

Tony