Yes the FamilySearch is the family.
But Bernard death cert in 1879 Annan has him as 74 (filled out by grandson, who knew Bernard's parents names and occupations) so his birth date is questionable. John Straney was an Irish weaver and possibly came over after 1797 uprising. They were from Down. The family also has 3 daughters dying in Carlisle 1803-10 so Margaret and Bernard may have been the only survivors.
Interesting about referring to Thomas as step-son, hmmmm, Ann's maiden name was Carr so maybe Bernard had suspicions about his parentage?

I like to think they had a sense of humour and kept the census taker on his toes!