Without knowing the exact date of Adelbert's death, a search through the newspapers would be quite time consuming. I checked a couple of sources in an attempt to determine the date of his death, without success. It is curious that the record of his death is apparently not in either of the Ohio death record databases that I searched. It makes me wonder if he could possibly have died in another state and was returned to Ohio for burial next to his first wife.
I did find a record that his second wife, Rachel (nee Curry), did file for a widow's pension after his death. Her pension application is dated May 9,1927 and was filed from Ohio. This would give a general time frame for his death as probably April or early May 1927. However, a newspaper search of that time frame in the Elyria Ohio newspaper failed to turn up an obituary. Of course he may have died earlier in the year, and she didn't file for several months. My experience however, is that a veteran's widow usually filed for a widow's pension within a few days of her husband's death. These were days before social security, and the veterans pension was often a main source of income.
I did find a brief biographical sketch on A.W. Mitchell in a 1916 History of Lorain County. I'm not sure that it contains much info that you don't already have, but I can send you a copy, if you wish. A few items from the bio are:
His parents were Peter and Catherine (Conklin) Mitchell. Peter was born in the North of Ireland in 1790, and Catherine was born near Kenyon, New York in 1815. They were married in New York, and came to Lorain County in 1844. The bio gives Peter's death as 1853 (maybe a typo), and Catherine's death as 1904. Peter owned 165 acres in Rochester at the time of his death.
Peter and Catherine had 16 children, Adelbert being the youngest. In 1916 only three of the children were still living. In addition to Adelbert, his brothes Sidney and Frank were still living. Frank was a farmer in Rochester Township, and Sidney a farmer in South Dakota. Adelbert worked as a blacksmith for 26 years before he purchased his father's old farm. According to the bio, he was living a comfortable retirement on 15 acres in 1916.
Adelbert's brother George was murdered March 13,1865 in Rochester, shortly after he was discharged from the army. He was with a friend of his who got involved in a dispute over some money, and when George intervened, he was shot and killed. His assailant was tried for murder, but was convicted of manslaughter. An Elyria newspaper from May 1865 has details of the incident.
Adelbert, Sidney, and George all served during the Civil War. The bio indicates that Adelbert was wounded in the battle of Peachtree Creek during the Atlanta campaign, andthat in 1916 he still carried the bullet in his body. His Civil War record fails to mention his wounding however.
Apparently Adelbert and his first wife, Dora (nee Vosburg) had only one child, a daughter Rena, who married Charles Call, who worked in a foundry in New London, Ohio. Dora died in 1885 and Adelbert remarried in 1887. His second wife was Rachel Curry, who was born in Troy, Ohio, but who had lived in Lorain County many years before their marriage.
Adelbert was a marshal in Rochester for seven years, and was a member of the village council for 17 years. He was a Republican in politics, a member of the G.A.R., and he and his wife were members of the Baptist Church.