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"...
There a couple independent guys who translate the twitter extras in the comments of pt's posts. Im just following the official serialization and Pt has these little twitter extras as, well, extras.
Didn't expect English speakers to fully understand 初夜 (directly translated to first night) without a note. There is the context of his mother being extremely unhinged but in Japanese it's a lot more explicit in its meaning for sex, thus me including the note. In English, just saying "first...
The author posts a 3-komas every couple of days on twitter. It's just like tidbits and slice of life stuff, sometimes the plots of those get devolpled more in the official publications and intergrated into the plot. There's often guys on Twitter who translate these 3-komas