Some time between 1872 and 1881 Frederick left Laura. Laura subsequently met a Charles Winkworth. They do not seem to have married. It seems only Laura's two daughters moved in with their mother and Mr Winkworth. Family legend has suggested that her two sons (Frederick and Alexander) went to an orphanage. However the 1881 records from the Saint Bartholomew’s Hospital (London) show Frederick was staying there (during the 1881 census) suffering from rheumatism. His address is given as 386 Bethnal Green Road, which was the address of his uncle Charles McGarrick. This suggests the boys may have been looked after by their wider family. Alexander seems to have been apprenticed to a porn-broker in Hanover Square.
I have scratched around and added a few bits but it is all a mystery! I have also sent a message to an Ancestry tree owner who hopefully may have some answers. If the children went into orphanages they may well have been sent to Canada, South Africa or Canada. Have yo got the 1881 census references for Frederick?
Seems that Frederick married Louise Ray in 1907 and died 25 July 1922 - I have added what I have found to his profile Frederick Joseph Farman