Thanks all for the response.
Looks like, my problem is now solved.
I got the agent to work on this. Air NZ has now reinstated our tickets from HK to Mum after submitting evidence like boarding pass of Cathay, immigration stamps, visa, etc proving we travelled on that flight.
After this, I have contacted Air India directly to reschedule the tickets for 25 Sep, which they have done for a nominal charge of Rs.1000.
The tickets are now confirmed and hopefully should not have other problem coming up.