Can you explain your request a bit more clearly.Maybe I,m having a senior moment but if this wife and daughter of Braithwaite died who is Wm H Horner?Its a bit confusing 
I think what is being suggested is that the Annie who married Henry Clarke Braithwaite is also the Mrs ? Horner on the passenger list with William Henry Horner and the infant Henry Horner.
And that on the 1911 census Henry Clarke Braithwaite was not
actually a widower - his wife had left him for Henry Horner, whose wife and child had died in 1907.
I hope this is the correct interpretation

As I suggested in my reply on the Durham Board, since you know that Henry Clarke Braithwaite was alive in 1911, you are unlikely to find a marriage between Annie Braithwaite and William Henry Horner between 1907 and 1908, and if a marriage did take place it would have been bigamous.