How to open a new form from another form

If I got you right, are you trying like this?

into this?

in your Form1, add this event in your button:

    // button event in your Form1
    private void button1_Click(object sender, EventArgs e)
    {
        Form2 f2 = new Form2();
        f2.ShowDialog(); // Shows Form2
    }

then, in your Form2 add also this event in your button:

    // button event in your Form2
    private void button1_Click(object sender, EventArgs e)
    {
        Form3 f3 = new Form3(); // Instantiate a Form3 object.
        f3.Show(); // Show Form3 and
        this.Close(); // closes the Form2 instance.
    }

In my opinion the main form should be responsible for opening both child form. Here is some pseudo that explains what I would do:

// MainForm
private ChildForm childForm;
private MoreForm moreForm;

ButtonThatOpenTheFirstChildForm_Click()
{
    childForm = CreateTheChildForm();
    childForm.MoreClick += More_Click;
    childForm.Show();
}

More_Click()
{
    childForm.Close();
    moreForm = new MoreForm();
    moreForm.Show();
}

You will just need to create a simple event MoreClick in the first child. The main benefit of this approach is that you can replicate it as needed and you can very easily model some sort of basic workflow.