Okay..
After you show the form set the visibility of the control to false.
Form1 frm = new Form1();
frm.MdiParent = this;
frm.Show();
btnShowForm1.Visible = false;
and on the form_closing event set the visibility of the control to true.
Suppose your MDI parent Form name is MDIParent1
then in the form_closing method
MDIParent1 parentForm = (MDIParent1) this.MdiParent ;
parentForm.btnShowForm1.Visible = true;
Prasant