The RI Cemetery Database has John's parents as Robert & Caroline (Knight) Remington, and says they are buried at Pawtucket. However, "Robert" should be "Albert D.," according to all other data I have found.
John A. Remington, MD, and Caroline N. Remington are both listed in the Central Falls Tax Book, 1921.
In the 1920 Federal Census, John & Caroline Remington are ages 52 & 43, living at Central Falls, RI. John is a physician. They have three children: Allen 21, Lawrence 18, & Carolyn 7.
Dr. John A. Remington received his training at Bellevue Hospital Medical College between 1888 to 1891. He became a successful physician in Central Falls. (see Representative Men & Old Families of RI, pp. 591 & 592)