I'm definitely not agreeing with Anakin in the PT movies, because he was a nasty, stupid, spoiled punk who screwed everything up massively because he threw a temper tantrum at not getting his way.

He had absolutely no good motives for what he did, either personally or politically. I doubt he even knew what he was doing. He behaved with all the self-awareness of a toddler with a soiled diaper.
I have nothing but the most thorough contempt for Anakin in the PT, and also for Obi-Wan, Padme, the Jedi Council and everyone else in the galaxy who were too moronic to see this obvious trainwreck coming. Only Palps behaved like a reasonably intelligent person although it's hard to have all that much respect for his manipulative skills either, considering how easy everyone made it for him.
However, TCW is confusing things mightily. Anakin is not being portrayed as he was in AOTC or ROTS. (Which is very confusing considering that TCW is
between AOTC and ROTS - it can't be a character arc, more like a character yo-yo.) He's far more emotionally stable, intelligent, and aware of the situation around him.
And the writers are making efforts to foreshadow
reasonable motivations for him to do what he did: he's learned that being the Chosen One means he is beyond the petty limitations of Jedi and Sith, with the implication being that, whatever "balance" means, he needs to do it on his own, and if the Jedi don't understand what he's doing, that's only to be expected.
They're also putting a lot more effort into establishing that the Jedi are on the wrong track politically and militarily. The Republic is definitely corrupt, so that even well-meaning, intelligent people would join the Separatist cause (it's a toss-up whether it's better to try to reform the Republic or just give it the boot and start over). The Jedi really aren't prepared to run a war, and the military officer caste of the Republic are getting restless about the screwed up situation. Anakin is seeing that the Republic might not be worthy of the Jedi, and that the Jedi might not be the right people to defend it, anyway.
The oddity is, this very interesting foreshadowing simply doesn't synch with ROTS, where Anakin's motivation was panic over Padme, stupidity and ego. To pay off the foreshadowing in TCW would require a run-through of ROTS again, except with a whole new set of motivations for Anakin.
As for killing the kiddies, that's still beyond the pale. Anakin as written in TCW would not do that. But the Mortis Arc also established that at least in some cases, and as far as we know, in all cases, the Dark Side is simply mind control. A person who falls to the Dark Side becomes a different person and does not know what they are doing.
So is this the "real" story? Faced with the knowledge that as Chosen One, he must act on his own, and having no faith in either the Republic or the Jedi, Anakin joins the Dark Side because he isn't afraid of it. The Chosen One is capable of controlling both Dark and Light Side. And he's also desperate - someone has to do something, and nobody else has the ability. But he underestimates his ability to control the Dark Side, and it ends up controlling him. From that point on, Anakin vanishes and is replaced by Vader. It's Vader who kills the younglings, not Anakin.
Padme has nothing to do with it. Notice how Anakin is not required by the story to be stupid, egotistical or immature. It's the classic Icarus myth - the hero who overestimates his abilities. It works great as a story, much better than the PT atrocity.