Beyond the security at the terminal entry gates giving you a runaround, this just seems like a rather unfortunate instance of IRROPS. Nothing about this seems particularly specific to India, so doubt if your wife could have helped much here anyway.

That being said, your bag should have been tagged all the way till final destination assuming all flights are on the same ticket (though you would still have had to collect it at DEL and go through customs and then re-check it with Indigo at T2).

I’m unsure about being able to skip the last leg from DEL to DED without it affecting the rest of the itinerary as LCCs like Indigo have their own rules about that. But on any legacy carrier, anywhere in the world, skipping the last leg of the outbound would have led to the cancellation of your return flights.

I don’t think there’s really much you could have done to make this better. It just seems as if it was a set of unfortunate events, exacerbated by Delhi’s fog situation and the fact that there was one person at the ticketing desk.