Reordering patches can be done by deleting and inserting a patch. Moving a patch forward (towards root of patch graph) is easier than backwards. In the former case you can skip the pbackout step.
You can also edit .hg/pgraph and then pmerging, but the existing .dep files will be left inside .hgpatchinfo. [pbranch 81fdb8ef32db] - I tried this and did have to do some manual cleanup afterwards.
It would be nice if TortoiseHg provided a GUI to ensure all necessary steps were carried out. Also, if conflicts occur it is important to be able to resume the pmerge process - the reorder operation must somehow be remembered so it can be continued. Perhaps with a bundle of all changes induced by the reorder.