Yes you can split the hive and it's fine to keep it in the same yard. Just divide it in half. If you can find the queen, great. If not, make sure that both halves have at least one frame with eggs or very small larvae on it. In a few days check to see that they have drawn queen cells in the hive without the queen (or if you hadn't found the queen, one hive should have cells and not the other). If you see cells, wait a month and you should have a new laying queen and be able to see uncapped brood.