Everyone would recognize their own father, whether young or old - so in Second Chance, why didn't the son recognize his own father Jimmy?
I haven't seen the show, but from what I've been able to ascertain seeing the commercials for it the premise of the show is that the father's consciousness is put into a younger body, but it's not a younger version of his body.
Wikipedia seems to agree:
The series follows the life of Jimmy Pritchard, a 75-year-old former King County, Washington sheriff who was morally corrupt and later disgraced and forced to retire. After he is killed in a robbery at his son's home, Pritchard is brought back to life in the improved body of a younger man by billionaire tech-genius twins Mary and Otto Goodwin.
Note that it says "the improved body of a younger man", which suggests it was a random body they had lying around, rather than a younger clone body of the father. If that's true, then the son doesn't recognise his father because he doesn't look anything like his father did, young or old.