How to reproduce:
public partial class Form1 : Form
{
    RadRichTextBox tb1;
    RadRichTextBox tb2;
    private bool shouldFocus = false;

    public Form1()
    {
        InitializeComponent();

        tb1 = new RadRichTextBox();
        this.Controls.Add(tb1);

        tb2 = new RadRichTextBox();
        tb2.Location = new Point(200, 0);
        this.Controls.Add(tb2);

        this.Load += Form1_Load;
    }

    private void Form1_Load(object sender, EventArgs e)
    {
        StyleDefinition style = new StyleDefinition();
        tb1.IsReadOnly = true;
        tb1.Document.Insert("text 1", style);

        tb2.Document.Insert("text 2", style);
        tb2.IsReadOnly = true;
    }

    private void radButton1_Click(object sender, EventArgs e)
    {
        tb1.IsReadOnly = false;
        tb2.IsReadOnly = false;
        tb1.Focus();
    }
}

Workaround:
public partial class Form1 : Form
{
    RadRichTextBox tb1;
    RadRichTextBox tb2;
    private bool shouldFocus = false;

    public Form1()
    {
        InitializeComponent();

        tb1 = new RadRichTextBox();
        tb1.GotFocus += tb1_GotFocus;
        tb1.LostFocus += tb1_LostFocus;
        this.Controls.Add(tb1);

        tb2 = new RadRichTextBox();
        tb2.Location = new Point(200, 0);
        tb2.GotFocus += tb2_GotFocus;
        tb2.LostFocus += tb2_LostFocus;
        this.Controls.Add(tb2);

        this.Load += Form1_Load;
    }

    private void tb2_LostFocus(object sender, EventArgs e)
    {
        shouldFocus = false;
        tb2.IsReadOnly = true;
    }

    private void tb2_GotFocus(object sender, EventArgs e)
    {
        if (shouldFocus)
        {
            tb2.IsReadOnly = false;
        }
    }

    private void tb1_LostFocus(object sender, EventArgs e)
    {
        tb1.IsReadOnly = true;
    }

    private void tb1_GotFocus(object sender, EventArgs e)
    {
        if (shouldFocus)
        {
            tb1.IsReadOnly = false;
        }
    }

    private void Form1_Load(object sender, EventArgs e)
    {
        StyleDefinition style = new StyleDefinition();
        tb1.IsReadOnly = true;
        tb1.Document.Insert("text 1", style);

        tb2.Document.Insert("text 2", style);
        tb2.IsReadOnly = true;
    }

    private void radButton1_Click(object sender, EventArgs e)
    {
        if (shouldFocus)
        {
            tb2.Focus();
        }
        else
        {
            shouldFocus = true;
            tb1.Focus();
        }
    }
}