I believe this should get you close enough to what you need:
$data = <<<DATA
<html>
<div class="mobile-container mobile-filter-container">
<div class="mobile-wrapper-header"></div>
<div class="mobile-filter-wrapper"></div>
</div>
<div class="mobile-container mobile-cart-content-container">
<div class="mobile-wrapper-header"></div>
<div class="mobile-filter-wrapper"></div>
</div>
<div class="unwanted">
<div class="mobile-wrapper-header"></div>
<div class="mobile-filter-wrapper"></div>
</div>
</html>
DATA;
$doc = new DOMDocument();
$doc->loadHTML($data);
$xpath = new DOMXpath($doc);
$elements = $xpath->query('.//div[@class="mobile-container mobile-filter-container"]/following-sibling::div[1]/@class');
echo $elements[0]->nodeValue;
Output:
mobile-container mobile-cart-content-container
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