When you move a shape in RadDiagram, all connections that are linked to this shape are moved as well. If you need to move just the shape without moving the connection, it is necessary to detach the connection. The attached gif file illustrates how to do this.
If it is not the case, please specify in details what is the exact requirement that you are trying to achieve. Thus, we would be able to think about a suitable solution and assist you further. Thank you in advance.
I hope this information helps. Should you have further questions I would be glad to help.