Richer and more intuitive tree
Use a proper tree, as in Tree Style Tabs, where any subtree can be dragged around, collapsed or closed. To fit groups into this model, surround groups with 'folders', so all groups are tree subtrees. These folders also provide a central place for all group operations. I suggest auto-naming the folders by listing their domains in order of first occurrence, though fussy users would be able to rename them. See mockup: http://tinyurl.com/tk-mockup-main
Instead of keeping the tab-look, the vertical layout could be just a normal hierarchical tree widget with lines showing the subtree level and "+" sign for collapsing or opening subtrees or folders. It would feel lighter.