Here is a code sample that demonstrates how to add a custom key-action mapping, and how to use the PerformAction method to do what you described here. Note that this is not necessarily a robust solution to your specific problem, but rather demonstrates some of the approaches you can take.

//  Add a mapping that activates the next row
this.ultraGrid.KeyActionMappings.Add(
    new GridKeyActionMapping(
        Keys.Enter,
        UltraGridAction.NextRow,
        0,
        UltraGridState.Row,
        SpecialKeys.All,
        0) );

//  Handle AfterPerformAction, and enter edit mode on the first cell
//  after the 'NextRow' action is performed.
AfterUltraGridPerformActionEventHandler handler =
delegate( object sender, AfterUltraGridPerformActionEventArgs args )
{
    if ( args.UltraGridAction == UltraGridAction.NextRow )
    {
        this.ultraGrid.ActiveRow.Cells[0].Activate();
        this.ultraGrid.PerformAction(UltraGridAction.EnterEditMode);
    }
};

this.ultraGrid.AfterPerformAction += handler;