You can't do that with DNS. DNS can be used to map domains to Ip(es). It cannot resolve a website to some specific URI.
You are able to accomplish this using .htaccess file. You can test adding following lines towards the file and find out whether or not this works.
RewriteCond % ^(?:world wide web.)?subdomain.domain1.com$
RewriteRule ^(.*)$ http://world wide web.domain2.internet/subfolder$1
RewriteCond % ^subdomain.domain1.com$
RewriteRule ^(.*)$ world wide web.domain2.internet/subfolder$1