In the case of this occurring after takeoff, that is the most critical phase of flight. The aircraft should be at its heaviest with fuel for the flight and then the rest. Still, all planes are certified to have a Max T.O. Gross Wt. Unless, that aircraft was above that limit then it should be controllable.

I still am perplexed by the look of the aircraft's movement in the last seconds. If it was not a model, it would have to be entering the early stages of a flat spin. That would happen if the aircraft approached its stall speed with one engine producing full power. That said, the crew could have still saved the aircraft at the point the video picks up the plane by reducing the power somewhat, lowering the nose and then increasing power as quickly as practicable and go back to flying. They had the river as their lowest elevation point to use for emergency ditching or level off and continue flying.

All that said, this still doesn't look like the same aircraft perspective-wise to me as what is shown or noted by the news. A shorter version of the A/C like the ATR 42 may be the actual type of aircraft. Hard for me to say by just looking at the bottom.

Still, crews practice until they are blue in the face in the US to handle such a situation. Could just be inexperience. One has to be cool in such situations as everyone's life depends on it.

CapnGriff