adding child nodes in treeview

It's not that bad, but you forgot to call treeView2.EndUpdate() in your addParentNode_Click() method.
You can also call treeView2.ExpandAll() at the end of your addChildNode_Click() method to see your child node directly.

private void addParentNode_Click(object sender, EventArgs e) {
  treeView2.BeginUpdate();
  //treeView2.Nodes.Clear();
  string yourParentNode;
  yourParentNode = textBox1.Text.Trim();
  treeView2.Nodes.Add(yourParentNode);
  treeView2.EndUpdate();
}

private void addChildNode_Click(object sender, EventArgs e) {
  if (treeView2.SelectedNode != null) {
    string yourChildNode;
    yourChildNode = textBox1.Text.Trim();
    treeView2.SelectedNode.Nodes.Add(yourChildNode);
    treeView2.ExpandAll();
  }
}

I don't know if it was a mistake or not but there was 2 TreeViews. I changed it to only 1 TreeView...

EDIT: Answer to the additional question:
You can declare the variable holding the child node name outside of the if clause:

private void addChildNode_Click(object sender, EventArgs e) {
  var childNode = textBox1.Text.Trim();
  if (!string.IsNullOrEmpty(childNode)) {
    TreeNode parentNode = treeView2.SelectedNode ?? treeView2.Nodes[0];
    if (parentNode != null) {
      parentNode.Nodes.Add(childNode);
      treeView2.ExpandAll();
    }
  }
}

Note: see http://www.yoda.arachsys.com/csharp/csharp2/nullable.html for info about the ?? operator.

May i add to Stormenet example some KISS (Keep It Simple & Stupid):

If you already have a treeView or just created an instance of it: Let's populate with some data - Ex. One parent two child's :

            treeView1.Nodes.Add("ParentKey","Parent Text");
            treeView1.Nodes["ParentKey"].Nodes.Add("Child-1 Text");
            treeView1.Nodes["ParentKey"].Nodes.Add("Child-2 Text");

Another Ex. two parent's first have two child's second one child:

            treeView1.Nodes.Add("ParentKey1","Parent-1  Text");
            treeView1.Nodes.Add("ParentKey2","Parent-2 Text");
            treeView1.Nodes["ParentKey1"].Nodes.Add("Child-1 Text");
            treeView1.Nodes["ParentKey1"].Nodes.Add("Child-2 Text");
            treeView1.Nodes["ParentKey2"].Nodes.Add("Child-3 Text");

Take if farther - sub child of child 2:

            treeView1.Nodes.Add("ParentKey1","Parent-1  Text");
            treeView1.Nodes["ParentKey1"].Nodes.Add("Child-1 Text");
            treeView1.Nodes["ParentKey1"].Nodes.Add("ChildKey2","Child-2 Text");
            treeView1.Nodes["ParentKey1"].Nodes["ChildKey2"].Nodes.Add("Child-3 Text");

As you see you can have as many child's and parent's as you want and those can have sub child's of child's and so on.... Hope i help!