Wow, the two parent pairs meeting actually happened much sooner than I expected. I guess it does make sense given the only chance is either before or after Youshin's parents leave for business. Better to say hi and try to get along with the future in-laws sooner.
Mama Tomoko to the rescue with that sensible suggestion. There's almost no way two hormonal teenagers who are dating and in a house where the parents are away will not try to do anything. Even Youshin himself is not confident he can hold back. As per mama Tomoko, he can just go to their house, and that also means Nanami's not at risk of getting attacked by perverts having to walk back home at night (even if Youshin will escort her). It's just inherently safer this way.
I love that Nanami's parents consider them engaged now and Youshin's parents accepted it fairly easily. The pressure on them to keep dating after the deadline is up just keeps on building: there are now more cons than pros to breaking up the "fake" relationship when the time is up.
On a side note I didn't notice this earlier but Mama Shinobu on page 6 seems to be much more... well endowed than at first glance. Maybe his parents are both good at keeping their power levels hidden. inb4 Youshin is also getting a new sibling a certain number of months from now after their business trip is over.