SSL through Apache Proxy - apache

Question

I have a server running lots of virtual machines, but only one public IP (and absolutely no way to obtain more). Many of these VMs use port 80 to display web content. At the moment, I use different ports to access these WebUIs, such as mydomain.com:9000, mydomain.com:7000, and so on.
What I want is to have subdomains, more like service1.mydomain.com, service2.mydomain.com...So I create a proxy VM onto which I redirect everything coming from port 80 and redirecting to internal IPs based on what the subdomain is.
Now my problem is the following: I have an SSL certificate from mydomain.com/www.mydomain.com. How can I set it up so the proxy propagates it? To me, the solutions are:
the certificate is on the proxy, so the proxy does this:
internal VM:http ---> proxy: http to https ----> outer world: https
the certificate is on the VM hosting the service and the proxy does not propagate the certificate, so the proxy does this:
internal VM: https ---> proxy https to http ---> outer world: http
the certificate is on the VM hosting the service and the proxy propagate the certificate, so the proxy does this:
internal VM: https ---> proxy: https ---> outer world: https
I'd prefer the last solution, but I don't know how to set it up on both Apaches, knowing that Apache on SSL-enabled VMs is configured as is:
<IfModule mod_ssl.c>
<VirtualHost _default_:443>
ServerAdmin webmaster#localhost
DocumentRoot /var/www
<Directory />
Options FollowSymLinks
AllowOverride None
</Directory>
<Directory /var/www/>
Options Indexes FollowSymLinks MultiViews
AllowOverride None
Order allow,deny
allow from all
</Directory>
ScriptAlias /cgi-bin/ /usr/lib/cgi-bin/
<Directory "/usr/lib/cgi-bin">
AllowOverride None
Options +ExecCGI -MultiViews +SymLinksIfOwnerMatch
Order allow,deny
Allow from all
</Directory>
ErrorLog ${APACHE_LOG_DIR}/error.log
TransferLog ${APACHE_LOG_DIR}/transfer.log
LogLevel warn
CustomLog ${APACHE_LOG_DIR}/ssl_access.log combined
CustomLog ${APACHE_LOG_DIR}/ssl_request.log "%t %h %{SSL_PROTOCOL}x %{SSL_CIPHER}x \"%r\" %b"
SSLEngine on
SSLProtocol all -SSLv2
SSLCipherSuite ALL:!ADH:!EXPORT:!SSLv2:RC4+RSA:+HIGH:+MEDIUM
SSLCertificateFile /etc/apache2/ssl/ssl.crt
SSLCertificateKeyFile /etc/apache2/ssl/ssl.key
SSLCertificateChainFile /etc/apache2/ssl/sub.class1.server.ca.pem
<FilesMatch "\.(cgi|shtml|phtml|php)$">
SSLOptions +StdEnvVars
</FilesMatch>
<Directory /usr/lib/cgi-bin>
SSLOptions +StdEnvVars
</Directory>
</VirtualHost>
</IfModule>
Thanks in advance ;)