nikagitte can mean limited to 明日に限って、割引します just for tomorrow, we are giving a discount
＊This is a compound particle to show that only X is different from others. It's meant to express an exclusive focus on topic item X. The predicate is either explicitly negative as in example #6312, or implicitly negative as in example #6313. An explicitly affirmative predicate cannot occur with に限って.
THIS IS WRONG: その日に限っていい天気だった。 (Only on that day, the weather was good.)
ex1 might be translated as "would be the last to"
The implication is that you wouldn't put it past _other_ children.
What about "would be the last to do" (sorry I'm not a native speaker of neither English nor Japanese)? Other forms: ~に限る with two meanings 1) resticted to, exclusively, only (女性に限る) 2) the best (夏はビールに限る)
i think this expresses a contrast, or slight exasperation. "I usually dont sleep in, but just this one day (when i had an interview) I overslept".
there isnt a direct single word in english for it. "of all days" / "just this day" / "particularly today"