As the previous commentator said, joke is Mitaka, in an attempt to sound cooler, mixed up all-nighter and one-night stand.
In the raws, Rentarou (the dad) said it was a "一徹夜" (Ichi tetsuya, TL: one all-nighter). Mitaka, wanting to spruce up the wording with English words, used "ワンナイト"...