Altere o nome de entrada para:-
echo "<td>".'<input type="text" name="date_from" class="datepicker">'."</td>"; // remove []
echo "<td>".'<input type="text" name="date_to" class="datepicker">'."</td>"; // remove []
Use o formato de data assim
Try: date("Y-m-d") which uses the numeric equivalents.
