I think Melissa being irritated is valid. As a reincarnator she knows best the culture in that world and women there are treated as nothing more than porcelain dolls. Although Nine is different Melissa perceives that Nine's worries is the same as thinking she's a weak woman. I mean she already prepared all possibilies and have life - saving items prepared so there's minimal harm. I understand Nine is worried but I still vote for Melissa.
I'm pretty sure you've seen how men adviced Melissa in the past chapters. They were more like insults disguise as advice. So I can understand why Melissa is irritated. Nine is also just a character albeit a mob character he's still from that novel.Melissa can't help but think "Does he think i'm weak too? A fragile porcelain doll?". Her plan might be reckless but it's a foolproof plan.
Her thinking that is understandable. Ofc she thinks its a foolproof plan cuz she's in the novel and knows everything even if nine didn't like her he would still be confused cuz why tf would you drink a deadly poison when it's deadly? But he likes her it's different than the guys that underestimated her and since she doesn't know it's complicated
Well, I do get Nine, actually. He loves her, and even if he was not in love with her, from his point of view, she is here saying she'll take a deadly poison. It's not just a minor thing. As someone said in another comment, Melissa knows Yuri's power, but Nine doesn't. So, her plan might just sound reckless to him.
On another note, women can be strong and powerful without being reckless and cluelessly marching forward. I get that people want Melissa to be this super independent person that doesn't care about what anyone says or thinks, but you can be powerful and humble enough to hear others and actually consider what they are saying. Completely disregarding what everyone says and thinks because of what she knows is not being a mega awesome woman, it is being arrogant and I mean that in a bad way (as some may think that is a good trait to have.)
I do love this manhwa, though. Almost everything about it makes me incredibly satisfied.