The parent-child relation should be declared using the DependendUpon tag in the C# project file (.csproj), like this:

<Project ...>
   ...
    <ItemGroup>
      ...
        <EmbeddedResource Include="Resources.resx">
           ...
        </EmbeddedResource>
        <Compile Include="Resources.Designer.cs">
            <DependentUpon>Resources.resx</DependentUpon>
            ...
        </Compile>
        ...
    </ItemGroup>
 </Project>