What you need is a Split functionality which is currently not implemented in TeamPulse but definitely is part of our Backlog. Also at this point there is no option to move tasks from one story to another.
I can suggest for your purposes another convenient way for managing stories. Currently we provide story relationship functionality. You can create one story (parent in your case) and few other smaller stories (child). When open them for editing, use "Stories" tab and link them to the parent story. During relationship creation use "Parent" relationship type. This way you can easily see related stories when use Hierarchical view (under Requirements -> View Stories) - they will all be displayed hierarchically.
Hope that help you.
the Telerik team