Sitemap.xml change home

you are getting that url because the homepage is a CMS page.
In your case it has the identifier home.
In order to change that url you need to rewrite the method Mage_Sitemap_Model_Resource_Cms_Page::_prepareObject and make it look like this:

protected function _prepareObject(array $data)
{
    $object = new Varien_Object();
    $object->setId($data[$this->getIdFieldName()]);
    //for home set url to ''
    if ($data['url'] == 'home') {
        $data['url'] = '';
    }
    $object->setUrl($data['url']);

    return $object;
}

of course this won't work if you change the homepage to an other page. But it's a quick way of doing it.
If you want the clean version you have to check what is the hompage for your current store.
For this add a new member and method like this:

protected $_homeId = array();
public function getHomepageId($storeId)
{
    if (!isset($this->_homeId[$storeId]))) {
        $pageId = Mage::getStoreConfig(Mage_Cms_Helper_Page::XML_PATH_HOME_PAGE, $storeId);
        $delimeterPosition = strrpos($pageId, '|');
        if ($delimeterPosition) {
            $pageId = substr($pageId, 0, $delimeterPosition);
        }
        $this->_homeId[$storeId] = $pageId;
    }
    return $this->_homeId[$storeId];
}

In this case, you need to modify the getCollection method in the same class. Before $page = $this->_prepareObject($row); add this:

if ($row[$this->getIdFieldName()] == $this->getHomepageId($store)) {
    $row['url'] = '';
}

Magento 1.9.0.0. added two events to adjust product and category XML sitemap:

• sitemap_categories_generating_before
• sitemap_products_generating_before

In Mage_Sitemap_Model_Sitemap::generateXml() they replaced

    foreach ($collection as $item) {

with

    $priority   = (string)Mage::getStoreConfig('sitemap/product/priority', $storeId);
    $collection = Mage::getResourceModel('sitemap/catalog_product')->getCollection($storeId);
    $products = new Varien_Object();
    $products->setItems($collection);
    Mage::dispatchEvent('sitemap_products_generating_before', array(
        'collection' => $products
    ));
    foreach ($products->getItems() as $item) {

Same for category pages, but 20 lines below they just kept foreach ($collection as $item) for CMS pages. I'd would adapt this method and rewrite/modify Mage_Sitemap_Model_Sitemap to replace it with ...

    $pages = new Varien_Object();
    $pages->setItems($collection);
    Mage::dispatchEvent('sitemap_cms_pages_generating_before', array(
        'collection' => $pages,
        'store_id' => $storeId
    ));
    foreach ($pages->getItems() as $item) {

---

Then you can use that new event to modify your CMS pages sitemap:

Event:

<sitemap_cms_pages_generating_before>
    <observers>
        <rename_home>
            <class>[model]/observer</class>
            <method>renameCmsHomePageUrl</method>
        </rename_home>
    </observers>
</sitemap_cms_pages_generating_before>

Observer:

public function renameCmsHomePageUrl(Varien_Event_Observer $observer)
{
    $collection = $observer->getCollection();
    foreach ($collection->getItems() as $item) {
        if ($item->getUrl() === 'home') {
            $item->setUrl('');
            break;
        }
    }
}

Thanks for the code.

Using this snippet, I have created an extension to automate this process. This will work with mult-store/site configurations too. In this extension, I have updated the CMS Sitemap link generation like the follows:

/**
     * Generate cms pages sitemap
     */
    $homepage = (string)Mage::getStoreConfig('web/default/cms_home_page', $storeId);
    $changefreq = (string)Mage::getStoreConfig('sitemap/page/changefreq', $storeId);
    $priority   = (string)Mage::getStoreConfig('sitemap/page/priority', $storeId);
    $collection = Mage::getResourceModel('sitemap/cms_page')->getCollection($storeId);
    foreach ($collection as $item) {
        /* Customizing sitemap generation where url key is home */
        Mage::log($item->getUrl(), NULL, 'SeoSitemap.log');
        $url = $item->getUrl();
        if ( $item->getUrl() == $homepage) {
            $url = '';
        }
        $xml = sprintf('<url><loc>%s</loc><lastmod>%s</lastmod><changefreq>%s</changefreq><priority>%.1f</priority></url>',
            htmlspecialchars($baseUrl . $url),
            $date,
            $changefreq,
            $priority
        );
        $io->streamWrite($xml);
        /* Customization ends */
    }
    unset($collection);

    $io->streamWrite('</urlset>');
    $io->streamClose();

    $this->setSitemapTime(Mage::getSingleton('core/date')->gmtDate('Y-m-d H:i:s'));
    $this->save();

    return $this;

You can find the entire source-code from my repository