<button type="submit" formaction="/transport/prigorod/<?=$keyFrom?>-<?=$keyTo?>/">Показать</button>
<form action="contact_process.php" ...> <--- а здесь указан верный путь к скрипту?
<input name="stationto" list="stationto" class="form-control" placeholder="Начните вводить">
<datalist id="stationto">
<? foreach ($station as $keyTo => $valueTo):?>
<option value="<?=$keyTo ?>" type="stationto" id="stationto" name="stationto"> <?= $valueTo; >
<? endforeach ?>
</datalist>