Hi,
We have the same scenario but ours is much farther in which production is in different city.
In our case we have setup an VPN or virtual connection.
From the production site we setup an Terminal Server (or you may Citrix) in which all
remote users will connect using RDC (Remote Desktop Connection).
RDC is the safest idea since if internet is disconnected from remote site, server is still running at the production and can prevent database corruption.
Your requirements will be :
1) Internet connection for site A and B
2) VPN connection (in our case we have an unified hardware which has a VPN, firewall, router and etc.)
Supplier of the hardware could assist you in this.
3) Terminal server at the production.
Hoping this could help you.
Regards,
Clint