Without actually being there, I would hone in on the ignition system. Bad spark plug wires and ignition coils contribute to those symptoms you described.

Check all connections throughout the ignition path to see if all is well. Check the plugs as well. Improper gap setting will impair performance under load.

After that, I would move on to the fuel delivery system. The filter is the cheapest (and most overlooked) cure for many fuel related problems.

I save the expensive engine management systems for last, after I've ruled out the lesser, more easily serviceable parts.

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2009 ML350 (106K) - Family vehicle
2001 CLK430 Cabriolet (80K) - Wife's car
2005 BMW 645CI (138K) - My daily driver
2016 Mustang (32K) - Daughter's car