Individual mailbox level sync as you ask is not provided for by MS or any other provider. This is why products like Citrix were created and why over 90% of fortune 500 companies use citrix and or products like it to do something similar to what you need done.
The common implementations for what you want (remote access to email given the exchange servers themselves cannot be on the internet)
1) Citrix Presentation Server/Suite. With MS TS licenses it works out to a little over $300/user. No server license costs other than base os.
2) Web/SSL VPN device. Various firewall/VPN devices (like a cisco ASA series or older VPN3000 series) will gateway a user into a DMZ where they can only access something like Outlook Web Access for email.
3) Put up another exchange server in a DMZ to act as a front-end server to provide outlook web access to Exchange (not the most secure idea any more given the connections needed into the LAN from the DMZ)
Another idea is just to give said users blackberries which doesn’t provide 100% same functionality, but it’s decent and very mobile.