What do you mean "the records show?" Whose records? Records of what?
There were three ships named Britannic. The last of them was in service for the White star Line from 1930-1960. This ship arrived in Boston on November 20, 1938. What is the issue?
The Scythia departed Liverpool, Greenock and Belfast on October 28-29 and arrived in Boston on November 6, 1938.
It would appear from the passenger manifest that all of your people embarked on the Laconia on October 8th in Liverpool and disembarked in Cobh.
They then reboarded the Britannic on November 13th for the journey to Boston. I don't know where you looked for a passenger list, but it is readily available from the usual suspects, NARA, FHC and ancestry.com
This was not the family's original immigration as they had been in the US since 1930, and the twins, John Albert and James Alwyn were born in Boston on 20 May, 1934. They were returning home to their residence on Savin St. in Dedham, MA, having left the US on September 5, 1938.