I have come across another programming challenge again and hopefully I wont close the thread myself this time.
I am expecting good suggestions or examples from you to do this.
I want to build a (scrollable) nested list, from which children of two parents could get swapped after some validation.
I intend to save this modification in the database too but later. To start with jquery code will do.
I haven't come with any code yet, but since I started working this, soon I would post my progress here.

Your suggestions are well appreciated to get me started quickly on this.

Thank you

You could give jsTree a look:
Click Here

It has a move_node event which contains old parent and old position information and a move_node method which you could use to move nodes programmatically.

Might be easier to modify the existing code to suit your needs instead of writing it entirely from scratch.