Getting Dunk-y with it

I think this is further corroborated by what Lyanna says of him in a flashback:

Lyanna's own reading of Robert is proven correct in the next line, when it's revealed how young the mother of Barra is believed to be. His inconstancy is a character trait he has always had, that Ned has refused to see as a persistent trait. This passage prompts us to question: how much of Robert's problems were always there, and how much was Ned unwilling to see it?

I think this is further supported by Stannis' own childhood recollection of Robert in ACOK, specifically in the scene about Proudwing:

Again, what's underlined here is that Robert values strength (not weakness), is socially rewarded for exhibiting strength, even if it is cruel and gratuitous, until he takes the role of king and finds himself - the representation of the charming, martial lord that westerosi masculinity adores - completely unfit for the role.

None of this particularly underlines the war as a point of change for Robert. Instead, the loss of Lyanna is suggested as a catalyst, as suggested by his blame-shifting:

War is something easy, something Robert is capable of. He 'killed him', and 'yet somehow he still won', despite the songs, despite the support of the masses.

As for whether Robert was capable of killing - or commanding the killing - of innocent children specifically, Ned himself is unsure:

Which to me suggests that's a can of worms Ned isn't willing to think about.

My sense is that putting all this evidence together, Robert is meant to represent someone who epitomises the martial prowess, physical strength, and laddish social graces that all make up the ideal of Westerosi masculinity. He is frequently described as unstoppable - in fact, this really indicates that no one really did stop him because they admired him for his excessive violence. I also think his treatment of women factors in precisely because a woman is a target of his excessive violence and because his attitudes towards women have never involved taking them seriously, viewing them as disposable objects who exist for his pleasure. The way he treats Barra's mother in particular is deplorable and not unlike how Robert treated Mya's mother - again, suggesting that he has not fundamentally changed, but rather that Ned's perspective on him is slowly becoming less idealised as the book progresses. Thus: War did not break him in this way. Rather, Robert represents someone enabled to be their worst by feudal patriarchy with no one challenging him ideologically.

As a result, Robert exists partially as a critique of Westeros' masculine gender norms and ideals. 'Strength', as a value, is questioned. We see this as a repeated theme throughout the series - indeed, that's something we return to with Daemon Blackfyre's martial prowess being contrasted to Daeron's 'soft belly' in the Dunk & Egg novella, and that idea of strength being core to leadership is something that we constantly take a critical view of in Jon, Samwell, and Dany's chapters in particular. What I'd say then is that it is not the Rebellion specifically that shaped Robert into the man he is, but instead the martial culture of Westeros more generally, both in peacetime and in wartime. War provides an opportunity for more gratuitous, morally abominable acts of violence, but the seeds for that are sewn much earlier.