We have 4 roundtrip business class tickets SFO-DXB-BOM flying out Dec 12, 2021 returning Jan 5, 2022, on a single booking. Emirates just changed our booking to put us on a Jan 6 flight from BOM-DXB that arrives in DXB after our DXB-SFO flight leaves, meaning we will miss our DXB-SFO connection. The tickets were booked through a third party travel site. Trying to figure out our options here.

When we called Emirates (the one time we were even able to get to an agent) they just said they can't change our tickets since they were booked through a third party site. When we called that site they are unable to find any seats on an earlier flight that allows us to make our connection in DXB, even if we look back as much as three days in the past, or find any seats on a later DXB-SFO flight.

What are our options here? The Emirates customer support number now just hangs up when we call saying that they are experiencing a high volume of calls. Shouldn't it be possible for the airline to make this right, even if the tickets were booked through a third party site? It seems like they shouldn't be able to wash their hands off the whole thing. Extremely frustrating.