Plugin/template embed parse order?

I’m in the middle of writing my first plugin and I’ve hit a snag. My code:

{exp:cwk_galleries:gallery perpage="9"}
    {exp:channel:entries channel="videos" sort="desc" status="open|comingsoon"}
        <div>TEST1</div>
        {embed="embed/video-gallery-entry" entry_id="{entry_id}"}
        <div>TEST2</div>
    {/exp:channel:entries}
{/exp:cwk_galleries:gallery}

My cwk_galleries plugin is supposed to parse the HTML via $this->EE->TMPL->tagdata and modify it in a few ways before returning the data. However when I return the data, it seems the template embed is getting stripped out completely. All that is returned is:

<div>TEST1</div>
<div>TEST2</div>
<div>TEST1</div>
<div>TEST2</div>
<div>TEST1</div>
<div>TEST2</div>
// etc....

Is there any way to achieve what I’m trying to do here? Or am I stuck hardcoding all of the HTML instead of using a template embed?