Magento – getChildHtml inside of another .phtml file

You can add a method on the parent block to fetch the child depending on the product type (I've seen this kind of logic a couple of times in core or something similar):

class ParentBlock 
{
    public function getIntuitiveNameChild($item)
    {
        return $this->getChild("intuitive_child")
                    ->setProductType($item->getProductType()) 
                    // You can also decide the product type in this setter, in the Child block.
                    ->setItem($item);
    }

    public function getIntuitiveNameChildDinamically($item)
    {
        return $this->getChild("intuitive_child_" . $item->getProductType())
                    ->setItem($item); 
    }    
}

// parent tpl
// i suggest you avoid getChildHtml(), unless you're certain that methods won't need to be called from the tpl
echo $this->getIntuitiveNameChild($_item)
          // ->someOtherMethod()
          ->toHtml();

Still, seeing how you modify the layout xml to add children blocks, you may be interested in how Magento decided to work with rendering markup depending on product types in Mage_Sales_Block_Items_Abstract::getItemHtml() and Mage_Checkout_Block_Cart_Abstract::getItemHtml().

Your layout xml should look like this:

<?xml version="1.0" encoding="UTF-8"?>
<layout>
    <default>
        <reference name="root">
            <block type="core/template" name="custom_block" as="custom_block" template="page/html/custom_block.phtml" />
        </reference>
    </default>
</layout>

But please don't output anything after </html>. It's wrong.