You will need to be able to get a remote connection to the computer you want to access.  That can be accomplished a number of ways, but you may need technical help to do it.

If you are on Windows Pro version, you can use the built-in RDP (Remote Desktop Protocol), but without a VPN (Virtual Private Network) set-up to run the RDP through, security can be a concern.  If you do set-up RDP, just make sure that the host computer opens up a different port than 3389, as that is the one most people use for RDP and port sniffers know that.  Use an odd port number that is not normally used for anything else, and make sure the host computer has an extremely strong Windows user password.  Then you would set up the RDP client on your home computer by creating a connection.  Computer:  The public facing IP address of the host, i.e.. XX.XX.XX.XX:Port# (the port # has to be specified after the colon, otherwise it will automatically use 3389 and you won't get a connection), and User Name:  MachineName\UserName.  You can find out what the public IP of any computer is by going to any site where you query "what is my ip address'?

Once you're on the computer, you would have access to the Quickbooks Desktop file that resides there.  If it's someone's computer that they need to be on, then any version of RDP likely won't work.  As soon as you remote in that computer, the host screen goes black.  Only one person at a time. :)  It would be great if they could host the QB file on a server or a low-use computer in the office so you can work on the file as you need to.  If they have multi-user access, then someone else can be on it at the same time as you, just not on the same computer.  If they don't have multi-user, then anyone else would have to exit QB in order for you to access the file.

There are other options that don't require setting up the RDP on both ends; i.e. TeamViewer, SplashTop, LogMeIn, pcAnywhere, GoToMyPc, etc.  Some of these are very strict about personal vs. business use, and if they even sniff that you are using it for business, they will kick you off the free version and insist you pay.  Chrome has a remote desktop as well, and it's free, so that is another option.

Hope you find a solution!