Here's the code that creates that filename path, found in Mage_Catalog_Model_Product_Image:
    // build new filename (most important params)
    $path = array(
        Mage::getSingleton('catalog/product_media_config')->getBaseMediaPath(),
        'cache',
        Mage::app()->getStore()->getId(),
        $path[] = $this->getDestinationSubdir()
    );
    if((!empty($this->_width)) || (!empty($this->_height)))
        $path[] = "{$this->_width}x{$this->_height}";
    // add misk params as a hash
    $miscParams = array(
            ($this->_keepAspectRatio  ? '' : 'non') . 'proportional',
            ($this->_keepFrame        ? '' : 'no')  . 'frame',
            ($this->_keepTransparency ? '' : 'no')  . 'transparency',
            ($this->_constrainOnly ? 'do' : 'not')  . 'constrainonly',
            $this->_rgbToString($this->_backgroundColor),
            'angle' . $this->_angle,
            'quality' . $this->_quality
    );
    // if has watermark add watermark params to hash
    if ($this->getWatermarkFile()) {
        $miscParams[] = $this->getWatermarkFile();
        $miscParams[] = $this->getWatermarkImageOpacity();
        $miscParams[] = $this->getWatermarkPosition();
        $miscParams[] = $this->getWatermarkWidth();
        $miscParams[] = $this->getWatermarkHeigth();
    }
    $path[] = md5(implode('_', $miscParams));
    // append prepared filename
    $this->_newFile = implode('/', $path) . $file; // the $file contains heading slash
So, the hash is generated from the configuration info (aspect ratio, etc), as well as the watermark info. This information will not usually change. However, I do see that the path is partially generated from the store_id of the current store, so your trouble may be there.
Is there a reason you can't let Magento use its normal caching procedures for both stores? Since Magento checks the filesystem for the cached image, there shouldn't be a conflict.
Hope that helps!
Thanks,
Joe
Upon contemplation, are you just trying to get the catalog images to work in both domains? The non-cached version of the catalog images are at %magento%/media/catalog/product. Copy the directories from that location and your catalog images should work.