Please refer this code
Ref:
I have added the Footer Template in the Child GridView.
Here is the changed HTML of GridView
<asp:GridView ID="gvCustomers" runat="server" AutoGenerateColumns="false" CssClass="Grid"
    DataKeyNames="CustomerID" OnRowDataBound="OnRowDataBound">
    <Columns>
        <asp:TemplateField>
            <ItemTemplate>
                <img alt="" style="cursor: pointer" src="images/plus.png" />
                <asp:Panel ID="pnlOrders" runat="server" Style="display: none">
                    <asp:GridView ID="gvOrders" runat="server" AutoGenerateColumns="false" CssClass="ChildGrid"
                        ShowFooter="true">
                        <Columns>
                            <%-- <asp:BoundField ItemStyle-Width="150px" DataField="OrderId" HeaderText="Order Id" />
                            <asp:BoundField ItemStyle-Width="150px" DataField="OrderDate" HeaderText="Date" />--%>
                            <asp:TemplateField HeaderText="Order Id">
                                <ItemTemplate>
                                    <asp:Label ID="lblOrderId" Text='<%# Eval("OrderId") %>' runat="server" />
                                </ItemTemplate>
                                <FooterTemplate>
                                    <asp:TextBox ID="txtOrderId" Text='<%# Eval("OrderId") %>' runat="server"></asp:TextBox>
                                </FooterTemplate>
                            </asp:TemplateField>
                            <asp:TemplateField HeaderText="OrderDate">
                                <ItemTemplate>
                                    <asp:Label ID="lblOrderDate" Text='<%# Eval("OrderDate") %>' runat="server" />
                                </ItemTemplate>
                                <FooterTemplate>
                                    <asp:TextBox ID="txtOrderDate" Text='<%# Eval("OrderDate") %>' runat="server"></asp:TextBox>
                                    <asp:LinkButton Text="Add" OnClick="AddRows" runat="server" />
                                </FooterTemplate>
                            </asp:TemplateField>
                        </Columns>
                    </asp:GridView>
                </asp:Panel>
            </ItemTemplate>
        </asp:TemplateField>
        <asp:BoundField ItemStyle-Width="150px" DataField="ContactName" HeaderText="Contact Name" />
        <asp:BoundField ItemStyle-Width="150px" DataField="City" HeaderText="City" />
    </Columns>
</asp:GridView>
C#
Onclick event of LinkButton. After saving the data i have refreshed the page to populate the added data.
protected void AddRows(object sender, EventArgs e)
{
    GridViewRow row = (sender as LinkButton).NamingContainer as GridViewRow;
    string orderId = (row.FindControl("txtOrderId") as TextBox).Text.Trim().Replace(",", "");
    string orderDate = (row.FindControl("txtOrderDate") as TextBox).Text.Trim().Replace(",", "");
    //Write code here to save these two variable data in SQL table
    Response.Redirect(Request.Url.AbsoluteUri);
}
Screenshot
