Charged for a non-existent airline ticket

I live in Cape Town. I booked a flight to PE for my wife and I to attend a wedding there on 22 March 2024. We had to change the flight times for the flight to PE from Cape Town, which we paid for through Vitality Travel, as they were the agents we used.

On arrival at PE airport for the flight home, Airlink informed us that there was no booking for my wife to return to Cape Town. My flight was valid.

After multiple phone calls and emails with every detail discussed, Discovery Vitality Travel said Airlink could not refund me and closed my query.

Vitality Travel took my money, and did not provide a ticket. This is *****ing.