I have exactly the same problem. The boy is supposed to shut down after Father says the code but he doesn't. This is why they are both 'busy', the script is stuck waiting for the kid to power off. None of the console commands to advance the quest or reset the AI do anything. I did get the quest to advance by killing Father and using the console to resurrect him, but this made everyone else in the institute hostile. This was funny, but not the outcome I wanted. Attempted to fix the hostility with other console commands but no success. Also tried various console commands on the kid but no joy. There doesn't seem to be a way to interrupt the running script. As far as I can tell from internet searches there is no solution reported for this bug. I've never had any problems with this quest before. The only difference this time around is the addition of Nuka-World DLC to my game, but I can't see why that would cause a bug in the Institute. Guess its back to Vault 111 to wait for the end of the world ..... again.