Everything in aired Torchwood canon really happened -- but that doesn't mean it has to happen again.
After the events of "Children of Earth", Jack travels back to just after Harriet Jones took office, planning to revert the Doctor's changes and preserve the original Golden Age timeline. How does he do this? Is he alone or is anyone helping him (Ten, John Hart, other time travelers)? Don't know, and it might be wise to avoid deciding until after the next Christmas special airs. But there's no reason we can't play with ideas before then.
What we do know is that the Doctor didn't do anything to Harriet that a thousand half-rate politicians don't try every day, and that a more experienced politician wouldn't have been able to defend herself against. Harriet didn't have much experience at that level of the political game; she was still thrilled over her recent victory, wasn't expecting attack, and didn't have the right damage-control mechanisms in place. But with a little bit of warning, she could have been prepared. She and Jack wouldn't even need to stop the vote-of-no-confidence from taking place; they'd just have to make sure she won it.
In "The Christmas Invasion", it's clear that Harriet knows more about Torchwood than an only-recently elected prime minister is supposed to. Where did she get that information? From post-CoE Jack, of course.
Now, he's not going to be telling her anything and everything. Telling her too much would endanger the timeline in all new ways. But he can tell her that if she doesn't complete her term, the vacant office will allow Bad People to come to power and that the results will be disastrous. And he can tell her enough about the Doctor and Rose to make her trust him, especially if he can get her access to Torchwood files about the Doctor and about himself.
The Golden Age timeline begins to diverge from aired canon when post-CoE Jack goes back in time, arriving sometime between "World War III" and "The Christmas Invasion". It doesn't begin to diverge in any major way until after the vote of no confidence fails. Canary Wharf still happens.
But with Harriet in charge, the aftermath of Canary Wharf is different. She's not going to allow the vultures of interorganizational politics to have quite as much fun shredding the remains of Torchwood 1 as they would have liked. The transition of power to Torchwood 3 will be just that little bit smoother. Slow-path!Jack will be just that little bit less stressed, less distracted, less preoccupied, knowing that the Prime Minister's office is supporting him instead of waiting to shred him when he slips up. And the woman still focused on health care issues in the middle of first contact is not someone who's going to let the survivors of Torchwood 1 be neglected, without appropriate counseling and follow up.
Ripples take time to become waves. Ianto still brings Lisa to Torchwood 3. Suzie still loses it. Gwen still joins the team. "Cyberwoman" plays out differently, causing its own ripples -- but those aren't large enough yet to prevent the Abaddon debacle. And Harold Saxon is still out there somewhere, making his own plans. What happens next? That all depends on those ripples.