When you do confirm that Joseph J. or John Joseph Archer was the father of Reinald I think the following is the record of when the mother died:
Amanda Maude Huard Archer
Rhode Island Deaths and Burials
Name Amanda Maude Huard Archer
Burial Date 26 Dec 1947
Burial Place P.Ocoag, R.I.
Death Date 22 Dec 1947
Death Place Woonsocket, Providence, Rhode Island
Birth Date 30 Aug 1876
Birthplace St. Anis, P.Q.
Marital Status Widowed
Spouse's Name John Joseph Archer
Father's Name Charles Huard
Father's Birthplace Canada
Mother's Name Virginia Bessett
Mother's Birthplace Canada
Note: If you check the 1900 census it shows her born Aug 1877 and in the death record it is Aug 1876, errors happen.
The attached is the family together in the 1915 RI State census. Note that this Reinald Archer in the 1915 census has the same job description, dresser tender, as Reinald Charles Archer in the 1917 WWI draft reg.
Good luck with the rest of search.