Please refer to the attached sample project and attached gif file which illustrates the desired behavior when RadForm1 is run. If you run RadForm2 which uses RadDropDownList, the binding doesn't work as expected.

Workaround:
this.radDropDownList1.SelectedIndexChanged += RadDropDownList1_SelectedIndexChanged;
this.radDropDownList1.DisplayMember = "Naziv";
this.radDropDownList1.ValueMember = "Id";
this.radDropDownList1.DataSource = bs;

private void RadDropDownList1_SelectedIndexChanged(object sender, 
    Telerik.WinControls.UI.Data.PositionChangedEventArgs e)
{
    if (e.Position > -1)
    {
        Roditelj parent = this.radDropDownList1.SelectedItem.DataBoundItem as Roditelj;
        this.radDropDownList2.DataSource = null;
        this.radDropDownList2.DisplayMember = "Naziv";
        this.radDropDownList2.ValueMember = "Id";
        this.radDropDownList2.DataSource = parent.Djeca;
    } 
}