BoB, but acknowledging that it might work out isn't quite good enough to actually take the step is it? When deciding whether to take a step that's going to have a massive social, financial and emotional impact on your life and that of your children, the bar to whether you do so or not has to be set as high as you can get it.
The OP is already set up quite well. She lives, not richly but reasonably. She manages her money, she has a good relationship with her kids, they're happy and stable, she's building on her training and education for a career. All this is something some people with formally better domestic set-ups might secretly envy her; so to risk it, it's got to be for something dazzlingly good and absolutely unambiguously better.
But that's not what's on the table here. This guy, even after the talk and the taking on board some of her points, doesn't look like an unambiguously better prospect for her. He's still got a long way to go to prove to her that it's a good investment of her time, energy, money and focus and in the best interests of her and her children, to live with him. He's nowhere near the point where it would be worth it.
I think that's why people are being quite vociferous about urging the OP to be risk averse. At 26 years old, she is incredibly young and has masses of time to decide whether to commit to this guy or not. And masses of time to find someone better tbh.
No one has to live with someone else. The problem is that it is the default mode of living so too many people ask themselves why they shouldn't do it - and in this case, there's a list as long as her arm - and don't ask themselves why they should do it. It shouldn't be something they do because he wants them to; it should be an active choice because not doing it would be unbearable for the OP and her children and she'd regret it for the rest of her life if she didn't. That should be the bar. At the moment, the bar's just nowhere near that.