question

@fzkim-3516, Welcome to Microsoft Q&A, based on my test, I reproduced your problem.

Please make the following changes.

First, Please set your treeview1 for the property TreeView1:

 public TreeView TreeView1
         {
             get
             {
                 return treeView1;
             }
             set
             {
                 treeView1 = value;
             }
         }

Second, we need to use Form.Show() Method instead of Form.ShowDialog(), because it will not update form1's control when we use ShowDialog() method to show form2.

 protected override bool ProcessCmdKey(ref Message msg, Keys keyData)
         {
             if (keyData == (Keys.Control | Keys.F))
             {
                 str = textBox1.Text;
                 Form2 search = new Form2();
                 search.Show();
                 return true;
             }
             return base.ProcessCmdKey(ref msg, keyData);
         }

Third, you could try to use Application.Openforms to transfer value between forms.

  Form1 form1 = (Form1)Application.OpenForms["Form1"];
             txtSearch.Text = form1.str;

Finally, Please refer to the following code example:

Form1:

  public partial class Form1 : Form
     {
         public Form1()
         {
             InitializeComponent();
         }
         public TreeView TreeView1
         {
             get
             {
                 return treeView1;
             }
             set
             {
                 treeView1 = value;
             }
         }
    
         public string str { get; set; }
         protected override bool ProcessCmdKey(ref Message msg, Keys keyData)
         {
             if (keyData == (Keys.Control | Keys.F))
             {
                 str = textBox1.Text;
                 Form2 search = new Form2();
                 search.Show();
                 return true;
             }
             return base.ProcessCmdKey(ref msg, keyData);
         }
    
         private void Form1_Load(object sender, EventArgs e)
         {
             treeView1.ExpandAll();
                
         }
     }

Form2:

   public partial class Form2 : Form
     {
         public Form2()
         {
             InitializeComponent();
         }
         //public delegate void ChildFormSnedDataHandler(string message);
         //public event ChildFormSnedDataHandler ChildFormEvent;
    
         private void button1_Click(object sender, EventArgs e)
         {
             Form1 form1 = (Form1)Application.OpenForms["Form1"];
             txtSearch.Text = form1.str;
             try
             {
                 TreeNode SelectedNode = SearchNode(txtSearch.Text, form1.TreeView1.Nodes[0]);
                 if (SelectedNode != null)
                 {
                     form1.TreeView1.SelectedNode = SelectedNode;
                     form1.TreeView1.SelectedNode.Expand();
                     form1.TreeView1.Focus();
                 }
             }
             catch (Exception ex)
             {
                 MessageBox.Show(ex.Message);
             }
             finally
             {
                 this.Close();
             }
         }
    
         private TreeNode SearchNode(string SearchText, TreeNode StartNode)
         {
             TreeNode node = null;
             while (StartNode != null)
             {
                 if (StartNode.Text.ToLower().Contains(SearchText.ToLower()))
                 {
                     node = StartNode;
                     break;
                 }
                 if (StartNode.Nodes.Count != 0)
                 {
                     node = SearchNode(SearchText, StartNode.Nodes[0]);
                     if (node != null)
                         break;
                 }
                 StartNode = StartNode.NextNode;
             }
             return node;
         }
     }

Tested result:

Best regards,
Jack

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