This is completely right At the moment it is all endorphins (discounting Bianca's illness). Alice thinks she is punishing Ioan by depriving him of the children, which she is, but she is also allowing a honeymoon period to solidify Ioan and Bianca's relationship. The rubber hits the road with the realities of everyday life and two upset children.
well, I'd say as long as those kids are upset this wont happen in the first place anyway
Alice said multiple times that she wanted them to break up, of course the public shitstorm option is in theory one way to do it, and she attempted to have the biggest reach possible for maximum hate
*, but it gives you the HUGE danger that they bond over this (which likely happened) and already experience very early in their relationship struggles that will make any future struggle easier to overcome (like the kids you mention), which I'm almost certain is also why Ioan and Alice lasted so long (parents not in favour of it, fans etc. - it's a softer version of the star crossed lovers trope).
A smart woman let's the upset kids go there to dampen the honeymoon period and kill off any chance to bond. A smart woman also would try to play it as gracious as possible because only THEN Bianca would reasonably feel guilt (regardless if they actually cheated or not, it eats you alive when the person that feels pain from you is nice to you), and only then most of the public would actually feel sorry for Alice.
*regarding the shitstorm option: even this she played absolutely dumb. She wrote a nice - albeit inconsistent as fuck - column about this, and had a pretty awkward interview (but like in the DM very focused on not blaming Ioan too much) on national TV that convinces probably everyone who doesnt know the backstory. She basically did here what I recommend above, but then you visit her twitter page and you see that she is an absolute shit lol. Either do it properly or not.