The problem here is you are not quite understanding how an ODBC connection works with access. We are not talking about a TC/IP or socked based connection here.
If you look at ANY connection string for an JET to access file, you see in the ODBC connection will always, I REPEAT ALWAYS include a fully qualified windows path name. When I say a fully qualified windows path name, I am talking to about a file that sitting on the hard disk.
At the end of the day we are thus talking about opening a plain Jane windows file. A horse is a horse is a horse and a windows file is a windows file, is a windows file.
In other words we are talking about opening a file sitting on the hard disk. So, this whole process is not any different than opening excel file, a text file, a PowerPoint file, or in this case an access file that just also happens to be sitting on the hard disk.
There's no server or particular database software that EVER has to be installed on the computer where this file sets. It is the CLIENT SIDE that must have the software and execute a standard windows file open command to pull the data off the disk drive. Remember when you place a word file on a server and open it, you never had to install word on the server, is the client side that's doing a windows standard file open, and the exact same scenario applies to JET when it opens a access file.
What this means then if you're going to open this file up over an Internet connection, you therefore must extend windows networking over the Internet. HTTP, or even FTP is nothing remotely close to the windows file networking protocol.
However, you can extend windows networking system over the Internet, and this is typically done by which called a VPN (virtual private network). That means you'll have to set up a VPN. This will thus allow you to see this other computer via network neighborhood and browse to the files on that folder on the server, and simply open it. Again your opening a standard windows file, there's not some type of service running on the server that you can connect to like with SQL server.
You can read the following article of mine and I explain why running a VPN over the Internet with windows networking and a JET (access) file simply will not work in an reliable fashion:
http://www.members.shaw.ca/AlbertKallal//Wan/Wans.html
So, just keep in mind that if you look at any JET ODBC connection string, you'll notice it's never a IP based, but must be a FULLY QUALIFIED STANDARD windows file name. I cannot stress and repeat again that we talking about a standard windows file name and location that we going to open.
Remember this is no different than opening word or excel or PowerPoint. The ODBC driver confuses this issue, since the driver is ONLY required to be installed and setup on the client side, there's nothing to connect two on the server side, except the required ability to open a standard plain Jane windows file.
What you thus ask as possible with a VPN, but not practical. You can read the above article and it explains in detail why this cannot reliably work and function.
With the advent of several free editions of SQL server, and so many other choices, the above limitation is likely not going to be an issue for you. These other server database systems are not file based, and your connection strings will NEVER resolve to some file name. And, thus these database servers also do not require the windows networking proto call to open that file, and therefore you can even connect to servers such as running linux etc. that don't even have windows networking installed. For a jet connection, you have to use windows networking to directly open the file .