There are many options you could use to do what you want.
To be able to connect to the remote PCs.
- To beable to connect to each computer you could you a service like GoToMyPC which places an small app on each remote computer and allows you to take over there computer at any time.
OR
- If they are running a Pro version of the OS like windows Xp Pro you could setup the computer with remote access and you could take over there PC that way. This method tends to get a like messy unless you have a static IP (yes you could use DDNS). Either way you could setup the routers to allow remote connection to their computers. Or if they happen to be there they can give you access. No this does have a security risk because you are opening a port of the firewall.
OR
Each site could have a router with VPN capibilites. So each office would have a VPN connection to you and you could remote desktop to them easlity through the VPN connection. This would of course require a device which allows VPN connection.
To share files
Each site could have a router with VPN capibilites. So each office would have a VPN connection to you and you could Share a folder on a computer at your location which each of them have access to. This option tends to get tricky because of having to manage all the VPN connections.
OR
You could use a service like the one below which allow file sharing over the Internet
http://www.filesanywhere.com/lp/onlinefilestorage.htm?gclid=CPrq7eLHn5wCFU1M5QodV10wfwhttp://www.egnyte.com/corp/on_demand_file_server_new.html?utm_source=google&utm_medium=cpc&utm_term=online%20share%20file&utm_campaign=Top+Converting&gclid=CLO4rfHHn5wCFRBM5QodsiR7fQhttp://sites.box.net/adwords/