Close Parent Form & open child form

Just hide Form1 rather than close it which, as you say, will close the whole application.

If you like, you can also make Form1 visible again automatically when Form2 closes with code such as this:

// in button1_Click

Form2 f2 = new Form2();
f2.FormClosed += new FormClosedEventHandler(MakeVisibleAgain);
f2.Show();
this.Visible = false; // hide Form1

// add this handler to Form1

private void MakeVisibleAgain(object sender, FormClosedEventArgs e)
{
     this.Visible = true;
}