Well to process PHP, the file must either be a PHP file or do .htaccess stuff (addhandler application/x-httpd-php .htm .html .rhtml) which will parse ALL files with .php, .htm, .html, and .rhtml extensions as PHP ... which you may not want to do, i don't know.
The question is, you say you can't modify the rhtml, how are you supposed to do what you want? You could do include("htmlfile.html"); in php in addition to the php code, but this will be very convoluted...
Do you mean that you have to leave the .rhtml as the extension?