Based upon the way Chiaki was involved in this, and other batsu game's, I'd be confident enough to say Chiaki divorced because of this hentai attitude, but she wants to help him get over it and get back to him.
Here's my psychoanalysis, bear in mind, I'm not a psychology major... and even if I were it'd be a mistake to take this with any level of sincerity.
In the first batsu after they were divorced, she introduced the "Shin-onii" gag, which I think could be interpreted a variety of ways... what I'd mostly go with is she wanted to instill guilt in him, plausibly seek revenge, but mostly convey "she's in demand" and that he should respect the fact she chose him... Either way, if she was really sick of him and didn't care anymore, she'd just leave and not come back ever again. So... while this mostly was done in anger and to vent frustration... it was a sign that from the beginning the divorce wasn't really because she wanted to... although its clear the shin-onii gag was done with pure malice in mind.
In subsequent batsu game's she's still showed up in different ways, which I think was her subtle way of reminding him of her presence. It's plausible she hoped he would come back for her with this reminders.
Two years ago, the nanpa incident is likely independent of this, as in his writing style you could tell the girl he tried to nanpa wasn't taking it well at all, mostly disgusted and disturbed, and probably reported it to the producers. The other nanpa incident was more likely something the producers had to research for as the girl involved had a more timid air about her that hints it wasn't something she volunteered of her own interest. With the tone and wording choice Chiaki demonstrated in this year's batsu it seems she worked with the producers to setup this scene for the ultimate emotional shock-therapy session to try and get Endou on the right path... the biggest hunch towards this was the Endou's mom laughing at the whole scenario which I think surmised because she was probably flattered that Chiaki is going to such great lengths to help Endou out... otherwise, this laughter might be an indication the parents don't take the matter as seriously... although I think its much more likely that Chiaki is going out of her way to help Endou than anything...
One other thing: There were a lot of subtle social ques that Endou was going to get a huge bash of embarassment later on in the show (foreshadowing)... a big reg flag being the same magazine showing up in the desks twice.
Finally, this "shock therapy" seemed to have worked on Endou, as when he got on the boat he zoned out and Hamada-san had to tell him to "pull himself together" for the quality of the batsu. At the time of the batsu game airing, it seems he has thought about the matter a lot since then, he is considerably more timid about the matter and in either months to come, or already has, asked for forgiveness from Chiaki at the very least... I think it is likely Chiaki and Endou will re-marry since this incident, however Endou also seems to be somewhat thick... and as for whether he will make the connection that Chiaki is making such great efforts for him or not is debatable... if he makes the connection that's where this likelihood to re-marry comes about, if he doesn't make this connection it's likely he'll stop being a hentai and show more respect towards women, but there also remains the possibility he gives into his hentai temptations and ends up hopelessly being stuck in a hentai mentality until an even greater social pressure shows up (by then it'd probably be jail time... hence the trial like atmosphere of this incident, a subtle hint by everyone what path he's on).
Bear in mind that he keeps saying "hochii" instead of "hoshii", it's kind of cute. In a childish/girly way. Hence massively embarrassing.
In my not-so humble opinion (that should be humbler), I think it's less the matter of being cute that's embarassing, but more the fact his cuteness was a "private" communication style only meant for the "nanpa" victims and for his private intentions to be exposed publicly is a greater embarrassment to his man-ego than to just come across as feminine. Although I agree though, that in doing so he presented himself in an almost submissive light towards the women, almost making them out to be his master with his desperation, which the reversal in dominance would be another blow to his ego's concern for his public image as a man. If anything, both were large contributors towards this "shock therapy"...