There is a property setting that you can use to cause the grid to wrap the row and move right on Enter.
this.gridControl1.Model.Options.WrapCellBehavior = GridWrapCellBehavior.WrapRow;
this.gridControl1.EnterKeyBehavior = GridDirectionType.Right;
Attached is a sample that uses these properties and does validation in CurrentCellAcceptedChanges without the double message.