Are Exercise event child events sorted?

In particular, are the events, as returned by an ExerciseEvent’s getChildEventIds in the order that the events are executed?

if they are not, what is the canonical way to put them into the order they were executed?

Yes they are ordered just like you would have created them in Daml. Note that this applies to getChildEvents and getRootEventIds. It does not apply to getEventsById on the tree, you have to traverse the tree to get the order.