Robert McArthur was a widower when he married Sarah Alward, a spinster, in 1876, although, where I have found records, his children born before 1876 said that Sarah was their mother. Perhaps Sarah was the only mother they knew - or perhaps Sarah had been married before and some of them were her children from a previous marriage.
Sarah was a widow in Summerside PEI in 1881 and 1891. In the 1891 census, the children all said their father was born on the Island.
Name Robert McArthur, widower
Event Type Marriage
Event Date 20 Apr 1876
Event Place Salisbury, Westmorland, New Brunswick, Canada
Spouse's Name Sarah Thompson Alward
Certificate Number 6650
Page 65
Citing this Record "New Brunswick Provincial Marriages 1789-1950," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:QVBF-K3HQ : 13 March 2018), Robert McArthur and Sarah Thompson Alward, 20 Apr 1876; citing Salisbury, Westmorland, New Brunswick, Canada, p. 65, Provincial Archives of New Brunswick, Fredericton; FHL microfilm 846,411.The death record for Sarah Smith said her parents were Atwood and Perry. In 1891, Sarah McArthur, widow, was living with Harriet, Loise [Florence?], James R., Jane McArthur (grand-daughter, age 6), and grand-sons Otis Robert and John Arthur Ramsay, aged 8 and 7, in Summerside, PEI.
Sarah later married Jacob Smith, and was living in Woburn Massachusetts with her son James Robert, and grand-daughter Jenny. In 1910, she and Jacob were in New Hampshire - on this census, they said they had been married for 15 years, and Sarah said she had 9 children, 8 living.
Her parents on her marriage were Charles and Mary (Perry).
Sarah was not in the 4 volume book about the Alwards of Kings County, NB.