I had the bug where the storage chest is missing in Hjerim.

I downloaded Hearthfire and purchased the children's bedroom set (new option) and the storage chest appeared.

I wonder if this fixes (or causes) the Breezhome Alchemly lab bug also?

I should add the chest appeared downstairs and not in the upstairs bedroom. Not really "fixed" but an acceptable workaround.

The chest comes with the children's room, so nothing was fixed. And considering we lost a wardrobe putting the room in, it was not that much of a gain. They just gave us back the storage taken for the extra room. None of which is anything to do with Dawnguard, that bug is part of the main game.