To unlock the "HAPPY FAMILY" trophy in Detroit: Become Human, you must make sure Kara Alice and Luther all reach Canada. It's unclear at this point whether all three can survive the river crossing in any scenario so I suggest playing it safe by going through border control. Besides, you can only get the below trophy for an official border control crossing:
Here is one example branch of the flowchart "BATTLE FOR DETROIT - KARA LEAVING DETROIT" to get Kara, Alice and Luther across the border, assuming you've managed to get Kara and Alice this far and Luther was saved during "CROSSROADS".
Bear in mind that this is one of perhaps many possible routes to getting Kara, Alice and Luther through border security. I will update with other options as they are discovered.
If you get Kara, Alice and Luther into Canada by the game's closing credits, you will get the trophy when you reach the flowchart screen.