Dear Friend,
When you click on the button to move the row from first grid to second grid then the first time the data gets visible into the second grid but when you again click on button to move the row from first grid to second grid then it overlaps the existing row. If this is your problem then you do one thing before moving the second row to second grid, store the second grid already added row into a datatable with same structure as the second grid and then merge this datatable with the row coming from the first grid.
dtsecond.Merge(dtone)
Please follow this link :-
Merge Datatable[
^]
Don't forget to mark this as your answer if it helps you out.
Thanks