You really don't seem to be listening to what the others are telling you, but I'll take a stab:
Yes, he gave in and used the Force to get his lightsaber and strike down the Emperor. His friends were dying, the Rebel Alliance was being crushed and hope was being extinguished before his very eyes. His desperation caused him to give in. At that moment Vader's blade blocked him and he withdrew. He fought long enough to break away and hide to avoid the fight. He resisted the lure of the dark side.
Then Vader goads him again, suggesting that Luke's sister will join them. At that point yes, he used the dark side of the Force in the final battle with Vader. He yells "Never!" and attacks Vader ferociously. He beats him. He takes Vader's hand. And then he SEES Vader's severed wrist. The wires and the machinery. He looks at his own hand and sees how much like his father he already is. How his anger has just brought him to THIS POINT. How his impatience in the past has already cost him. And the Emperor is laughing and telling him to kill his father and take his place at the Emperor's side.
And at this point, he pulls away from the dark side and does what his father couldn't do before him. He renounces that darkness, throws away his own lightsaber, commits to the light side of the force and accepts his own fate, even if it means he dies.
He is a Jedi. Like his father before him. But better.
I gotta say, that scene in the movie, as well as the way you just described that, always gives me goosebumps. It is really quite interesting the symbolism that is presented in that short time frame. And I think that through your explanation you hit the nail right on the head.