Yep, weakref’s excellent here. Specifically, instead of:
self.children = {}
use:
self.children = weakref.WeakValueDictionary()
Nothing else needs change in your code. This way, when a child has no other differences, it just goes away — and so does the entry in the parent’s children map that has that child as the value.
Avoiding reference loops is up high on a par with implementing caches as a motivation for using the weakref module. Ref loops won’t kill you, but they may end up clogging your memory, esp. if some of the classes whose instances are involved in them define __del__, since that interferes with the gc‘s module ability to dissolve those loops.