No, the tv series can't repair the damage done by the prequels.
I will always see Anakin as a whiny, pretty boy who went to the dark side and killed countless other jedi because he had a bad dream about losing his spouse. Not ambition, hatred or greed but a silly attempt to stop a premonition of his girl dying. I guess Lucas wanted to make Anakin's transition to the dark side somewhat noble but betraying the jedi order and becoming a sith shouldn't be noble at all. It should be a morally bankrupt decision through and through.
Sorry but nothing about Darth Vader's origin embellishes or improves the character. In fact, everything about Anakin is a disappointment.
The Clone Wars makes Anakin somewhat less laughable but it's too little, too late.
See the problem again isn't what Lucas did it's preconsived notion of why Anakin turned to the Dark Side. You wanted there to be some big dark reason such as a for power and ambition. Instead you got something else.
You're right Anakin was a whiny teenager who thought he knew better and that the older wiser grown ups around him knew nothing. Let me tell you secret that's not uncommon in Teenagers. Granted it's a bit over exaggerated but not uncommon to a degree.
Anakin's initial turn was to save Padme life. However as episode three progress past that point his reason for the turn change. It become less about saving Padme and more about gaining more power. I'll tell you why this happen.
Anakin turned to the dark side to save Padme. He sacrificed himself for what he believed to be the greater good. However I really believe that he though he could go over to the dark side and not loose himself but that is exactly what happen. However there was still a shred of goodness in him. It was why he was making a plea to Padme about ruling the galaxy together.
When he finds out Padme is dead and his vision was full filled all aspects of Anakin vanished until he finds out about Luke. This is the Darth Vader that we see in episode 4. He older and been through more so his personality will be different but for most part that is the same Vader. Only we don't really get to see that Vader.
Now when you get to empire Vader finds out that the person that destroyed the Death Star was Luke and that he had a son. This awoke something in Vader that he thought was long gone. It awoke his true self; Anakin Skywalker. What we see is a back paddle from that point on. He makes the same exact plea with Luke that he made with Padme.
What Lucas was trying to do was show the tragidy of Anakin Skywalker. He wanted fans to see a man who was good but had a lot of flaws and made a lot of bad choices that cost the universe. He wanted us to see the man not the machine that we see in ep 4-7.
One other thing I want to point out and then I need to leave. When Anakin left to become a Jedi he grew up from that moment on hearing about the prophecy. He grew with every one having this expectation of him to do all these great things. It had to have weighted on him a great deal. This is part of the reason why he was so frustrated in EP 2 after his mother death. He had all this power and yet he was powerless to stop her from dying. Imagine how frustrating that could be. He blamed Obi-Won for holding him back even through apart of him knew it wasn't Obi-Won fault.
Anakin is a tragic character and that was the point of what Lucas was trying to show. Vader was a villain that had no motivation other then serving the empire and that was the point of the character. When you get to Return of the Jedi it is the two characters at conflict with one another. The fight between the death start with Luke, Vader and Emperior is an internal fight and less of an external fight.
Any way that is my take on it. I have to run.