How to query children by post name/slug

Try using the get_page_by_path() function (Codex ref).

So, something like:

$mypage = get_page_by_path( 'page-slug' );

$mypageid = ( $mypage ? $mypage->ID : '0' );

Then, the post_parent argument becomes:

'post_parent' => $mypageid

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