The most likely suspect is the generator. Have it professionally load-tested. If it can only produce around 30 - 40 amps, which is exactly one third of its design rating, and "ripple" is very high, it has a bad diode. The voltage spikes these poorly designed generators produce destroy the internal diodes or voltage regulator, and those spikes can interfere with computer sensor signals and result in engine running problems. It is common to go through four to six replacement generators in the life of the car. To reduce the number of repeat failures, replace the battery at the same time unless it is less than about two years old. As they age they lose their ability to dampen and absorb those harmful spikes.
You can also get clue verifying this by unplugging the small connector on the side of the generator. Proof will be the engine starts running better.