It seems I've found the legal justification for the POTUS to attack the housebot full of Cumberland citizens.
Essentially, the Cumberland citizens are human shields, even if that wasn't the explicit intent of King Radical. If a nation is party to the Fourth Geneva Convention, this would be illegal. However, it's doubtful that King Radical is party to the Fourth Geneva Convention, although he will probably be roundly condemned for putting the Cumberland citizens in danger. It is apparently viewed that any nation may protect itself, and thus attack an attacker even if there are human shields involved. The defending nation should try everything it can to avoid hitting the human shields, but if any die, the onus is on the attacker, not the defender, for putting the non-combatants in harm's way to begin with.
King Radical started this battle when he attacked the tanks, helicopters and jets, culminating with attacking the POTUS herself by dumping her and her Secret Service agents from a lethal height during a surrender negotiation.