How do you programmatically reorder children of an ATFolder subclass?
Quickest solution: subclass from ATFolder instead of BaseFolder. That gives you all the "normal" reordering and other commmon plone folder capabilities (which I suspect you also want).
If you want to be more selective, look into Products/ATContentTypes/content/base.py: ATCTOrderedFolder and OrderedBaseFolder.
I have Plone product that uses a custom folder type for containing a set of custom content objects.  The folder type was created by subclassing BaseFolder and it has a schema with a couple of text fields.  Currently, when custom objects are added to the custom folder, the objects are sorted alphabetically by their id.  How can I override this behavior and allow my users to sort the custom folders manually, say through the "Contents" view?