I haven't tried this, but taking a look at the tab controller, I think I'd try out the GetNextFocusableControl method of the controller. Then to make this more usable, I'd add a property to your groupbox to set the controller.
Private _controller As TabController
Public Property Controller As TabController
Get
Return _controller
End Get
Set(value As TabController)
_controller = value
End Set
End Property
Private Sub GridGroupbox_Leave(ByVal sender As Object, ByVal e As System.EventArgs) Handles Me.Leave
Me.Controller.GetNextFocusableControl(Me).Focus()
End Sub
The GetNextFocusableControl method returns the next enabled, visible control in tab order, as defined by the tab controller, relative to the control passed in. This can get confusing, so likely you'll need to tweek what control is used (likely it won't be "Me", but one of the controls within the group box).
Also, using the technique your using, rather than store the control name (which might change), make the property of type Control. Then you can select the control from those on the form.
Private _NextControl As Control
Public Property NextControl() As Control
Get
Return _NextControl
End Get
Set(ByVal value As Control)
_NextControl = value
End Set
End Property
Now you can use Me.NextControl.Focus() to set focus on that control. Have fun playing with this.