Chase My Friend,
You are close but not right on. General Barlow and his mother lived at Brook Farm for a time like you say, but, Robert Shaw was not there at that time. There is a connection tho. Francis Barlows first wife Arabelle was a nurse during the war and died while in Service to the country and its men.
You of course know the story of General Barlow and Confederate General John Gordon. How Gordon found Barlow severly wounded on the battle field, carried him to shade and gave him water to drink. Then Barlow asked for his wife and Gordon allowed her to come to tend to her husband under a flag of truce. They were reunited sometime after 1865. Gordon and Barlow that is.
After General Barlow lost Arabelle, he married a second time to Ellen Shaw. I am not 100% sure on this but I think she was Robert Shaw's sister. In any case they named thier first son, Robert Shaw Barlow. I have always assumed that is why he was given that name. Also, at one time Robert Shaw was a student of Mr. Barlow. I assume once again that since they were all Unitarians that must be the connection.
Sorry to be so wordy.
Frank