Hypocrisy Nod: Both Hiccup and Mirabel realize that they are starting to sound like Stoick and Alma and their frustations with them before deciding that they should stop thinking like that before History Repeats itself.
A twinge of familiarity. An irritating itch, that told them that they’ve heard these things said before. In regards to certain other kids. In a different time. One so far in the past that it was no longer very relevant to their daily lives. Yet it was still so formative to their development. There was a period where they couldn't imagine their lives as anything different. His life as a scrawny, useless Viking. Constantly being told by his village and his own father that he was a walking disaster. Her life as the gift-less blunder. Constantly being asked by her abuela to step aside, with the implication that she wasn't as important as the rest of her family ringing loud and clear. Every day, for years, they'd heard these things. Felt these things. And they’d just said them about their own children. The realization hit like a blow to the stomach. The couple felt winded by the very thought.
The things Hiccup and Mirabel rant about their kids are, ironically, things Stoick ranted to Gobber about him; how different Peep was "since she could crawl", how Pedro has the attention span of a Sparrow and Karla's inability to listen to anyone and cause chaos as a result, leaving them to clean up after her.
Mirabel also realizes that she sounds just like Alma when she wished her kids would "step aside" so that they could run the town without the chaos they cause.
The Last Straw: As frustrating as their kids could be, the Quaken Incident was this for Hiccup and Mirabel, being cranky and irritable for the rest of the day before venting to each other in their bedroom.
Parents as People: Hiccup and Mirabel are quick to realize that they are starting to think like his father and her grandmother respectively and briefly wonder if that makes them bad parents before deciding to correct that issue.