Zend certified PHP/Magento developer

Magento 2 layout XML reference block added in CMS page

I have a CMS page, and in certain place it references a custom block from my module as such:

{{block class="MyNotificationBlockNotificationForm" name="notification.form" template="My_Notification::form.phtml"}}

This works and shows the template, but I don’t know how to define child block within this template. In my module I have view/frontend/layout/default.xml:

<?xml version="1.0"?>
<page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd">
    <body>
        <referenceBlock name="notification.form">
            <block name="notification.form.inner" class="MagentoFrameworkViewElementTemplate" template="My_Notification::inner.phtml" />
        </referenceBlock>
    </body>
</page>

and in my form.phtml I have

...
<?php echo $this->getChildHtml('notification.form.inner') ?>
...

but it just doesn’t show up. I tried various other things, including trying to use addChild() in my block class constructor, but no matter what I try it just doesn’t show up. What am I doing wrong?