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If both heater core hoses are hot with the engine running and heater on high heat or very warm to hot to the touch this isn't a heater core issue here.
This is due to a fault internally in the heater box itself.I only see you have one air mix door so this controls both the driver and passenger side heat.I suspect this actuator is o.k. since you do have the heat on the driver's side as well as air flow.
But there is a restriction internally in the heater box itself causing this issue.This can be a door that came loose internally or foam internally coming loose blocking temp and flow as I have seen in most cases.I have had to remove the heater box from the interior of the vehicle and take it apart to locate what is causing the restriction issue.
Now if one heater core hose is hot and the other is allot cooler then this is a heater core fault and since it has been flushed and still does not work properly the heater core will have to be replaced.
It will be one of these two things here that are causing this fault needing repaired.
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