This is the right family in the 1910 census, but I can't find a Joseph.
I did find an inconsistency that indicates family stories are correct.
Annie was 13 on the 1910 census, listed as a step-daughter. Her birthplace was listed as Pennsylvania. Her mother immigrated in 1900 according to the census. So, she was either born abroad, or her mother immigrated before 1900.
Family stories state Mary was widowed and immigrated with Annie when Annie was 2. If Mary immigrated in 1900, it sounds like that is what happened; Annie wasn't born in Pennsylvania.