without you giving us more information on what your code is doing systematically and practically (code snippets) it is impossible to give you any reasonable advice; will end up in pure speculation.
Your problems do not clearly fall into one category of possible causes for the described behaviours. Especially the viewport related ones are odd, since a generator should be static regarding viewport operations, rely on its cache, unless you have specifically designed it to operate otherwise.
NodeData::CopyTo() usually has only to be implemented when you have to alter data of your node when it is copied. Which could be the case for you, depending on how you handle your "alembic-like caching format", but should neither be needed for renaming nor copying in "normal" cases.