All of this assumes that this is just a text box somewhere on your page, and not in a DataBound control. If the text field is part of the itemTemplate element in the repeater, and Child_ID is what differs in the data row, then all this is wrong.
Do this instead:
<asp:TextBox ID="TextBoxChildID" runat="server" Enabled="false"><%= Child_ID %></asp:TextBox>
In short, you are making the same mistake I made when I asked this question: Why does <% =%> work in one situation, but not in another
Alternatively, in code, you can have this in your ASPX:
<asp:TextBox ID="TextBoxChildID" runat="server" Enabled="false"></asp:TextBox>
and this is in your code behind:
TextBoxChildID.Text = Child_ID;
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