The code you show doesn't embed Form3 inside Form2 - it embeds it in Form1 alongside Form2. If I simplify your code:
var f2 = new Form2();
...
this.Controls.Add(f2);
var f3 = new Form3();
...
this.Controls.Add(f3);
What you would need to do is:
var f2 = new Form2();
...
this.Controls.Add(f2);
var f3 = new Form3();
...
f2.Controls.Add(f3);