In the MDI Engine application the following error is thrown when the zoom control is added to the toolbar placed on the child form at design: "Unable to get the window handle for the 'AxToolbarControl' control. Windowless ActiveX controls are not supported".
If toolbar needs to placed on the child form then zoom control can be added programatically in Form_load event of the child form and re-set the buddy control of the toolbar:AxToolbarControl1.AddItem("esriControls.ControlsMapZoomToolControl", -1, -1, False, -1, ESRI.ArcGIS.SystemUI.esriCommandStyles.esriCommandStyleIconOnly)AxToolbarControl1.SetBuddyControl(AxMapControl1.Object)