It's truly glorious that what's in the "best interest of the children" is whatever matches the stranger outsider's philosophical goals. Of course who could argue with "engagement." That sounds great! The devil of that is in the details, and not necessarily mean anything approaching equal time spent child-rearing. "Interest of the children" spoken by some outsider to try and force others to act towards their philosophy, might be responsible for more atrocities and misdeeds than anything else in history.

Personally I don't take your omniscient approach. I believe the parents are nearly always better position to determine the interests of their children than some random dude on HN, than the outsider trying to impose their goal of their particular vision of "engagement."