I don't have a problem with her having a kid from a prior relationship, but it really does bother me that Gon is being portrayed as if he made a mistake for hesitating after learning about it.
Hell, it would be more irresponsible if he had immediately said he was okay with it.
I'm not so sure that it's being portrayed that way - at least in absolute terms. What he did hurt their relationship, but I don't think he's being portrayed as wrong for doing it. Gon-chan certainly thinks he did wrong, but that's because he cares about his relationship with Kaori.
One of the big recurring themes in this manga has been that different things matter to different people - and marriage means different things to different people. What people value is rarely clearly depicted as wrong. But it's acknowledged that differences in what we value makes two people more or less compatible. It's how we navigate those differences that makes any relationship, up to and including marriage, possible. The characters are still figuring out what their relationships mean to them, and in the afterwards, the author has even admitted that he doesn't have a great idea of where this is all headed. Most of the time, this work feels more analytical than anything else. It asks more questions than it gives answers, and the answers tend to be tentative and may only apply to certain kinds of people. That's a big part of why it has so much soul - it's unabashedly sincere and very thoughtful. The only hard message seems to be that people need to be honest with themselves about who they are and what they want from a relationship, because any relationship built on lies (including self-deception) is inherently unstable. But that's just kinda obvious.
The only time I ever felt like an authorial judgement call was being made, was when Rika's mom got involved, and she started trying to mold Takuya into her image of the ideal young man. It was fake. It was insincere. But that too could just be a consequence of the characters, rather than the author inserting a judgemental tone. Given how it seems to contradict one of the core messages - you need to pursue and be honest about what you value from a relationship, be who you are - I think there was some judgement there.
That said, I agree that Kaori is being unreasonable for expecting an immediate turnaround following that kind of shock. I think her refusing to give him a second chance and sending her friend in her own stead was unreasonable - and rude. No doubt, she hurt Gon-chan as much as his silence hurt her. He fretted over what he did and cried over her, and she didn't show much compassion for his suffering. That's unreasonable. In this chapter, she even apologizes for saying something unreasonable - her genuine (and unreasonable) feelings. I wouldn't be surprised if their subplot concludes with them both realizing that have some personal issues to work through. For his part, Gon-chan needs to be more confident and secure by himself, and more comfortable expressing himself. Kaori needs to have more reasonable expectations, especially for Gon-chan, who's never had to deal with feelings like this before, and hasn't had the life experience which taught her how to navigate these relationships.
And that's my multiparagraph analysis of this mongolian anime.