Plesk uses PHP’s open_basedir setting to restrict PHP scripts to their domain’s httpdocs directory (and /tmp) for security. If you check the domain’s error_log you’ll see that the open_basedir restriction is in effect (or enable display_errors to see errors in your browser, but this is not recommended for production sites).
You can override a domain’s open_basedir setting if you want, for instance you can add domain2’s path2 directory to domain1’s open_basedir like this:
<Directory /var/www/vhosts/domain1/httpdocs> php_admin_value open_basedir "/var/www/vhosts/domain1/httpdocs:/tmp:/var/www/vhosts/domain2/httpdocs/path2" </Directory>
See Including Directives into Web Server Configuration File for instructions on adding custom Apache settings for a domain.