Unfortunately, when you talk about a cross-country connection, you are running major risks by doing data sharing across that network. You are at the whim of lots of factors.
If you get charged by your ISP by the kilobyte, you will incur some really UGLY charges because of the way Access abuses networks for remotely-held files.
Stuff transmitted across a cross-country network is visible by folks who have learned how to tap into passing network traffic. So if there is mission-critical or proprietary data passing along, you are exposing it to the world.
Synchronization across a cross-country network is going to be limited by the slowest link in the network chain between here and there. So you would see pretty poor performance based on that remote data sharing.
My advice to you is that you CANNOT use a single database in this situation if you are bound to Access on each desktop. You MUST include a way to reconcile separate databases on a regular basis, then transmit your reconciliation data as transaction records in a burst mode that minimizes sustained traffic.
This assumes that you don't have something like a direct and private OC3 or DC12 network link among all of your separate sites. If you DO, then the prior arguments aren't so important. But given the big bucks involved with that level of network connection, I'm betting that you don't have that hot a data pipe. If that is the case, you are pretty much hosed with regard to remote data sharing.
Now, there is another way... still ugly but at least doable. If every user MUST see the same data, you can do it through the web. You need a special set of licenses to make it work with Access, but it can be done. Make the hottest server of the bunch the master server for all sites. Then create a bunch of Active Server Pages to provide your forms and other data at that site. Secure it with the something like OpenSSH or one of the other secure transmission layers. Put up a web site that controls access to those pages, give it a good login shell.
Unfortunately, when you are talking "long-distance remote" and "Access" in the same breath, you aren't talking cheap, convenient, secure, or efficient. It is just the nature of the beast.