Yes, it has to to with the domain. When your pc is part of a domain you cannot join a workgroup at the same time. It's either or. What I would try to do if you can is to set up an ftp server on the work pc if you have permissions to install software on it. Then you should be able to access the computer via ftp instead.
Of course this all moot point since i have the situation backwards.
Now, for your issue it it could be a few things that could be preventing this from working out.
First and foremost, it could be the ports that you use to connect to the home computer are being blocked by the work place firewall (if they have one and if you are trying to connect remotely). If this the case then there might not be too much you can do about it, beyond connecting the work computer to the network.
Another reason why this could be failing is that you don't know how to reach your home computer remotely i.e. you don't have what's called a static IP address or dynamic DNS installed on your home computer. This issue is much easier to solve: either install dynamic DNS on your home computer or pay extra for a static IP address. Be aware however, that people do scan and probe both so be sure to have some kind of firewall somewhere.
You haven't elaborated much on the service that your trying to use beyond file transfer so i'll assume that you are doing just that, you want to be able to transfer files from your home to the work computer. However if your trying to use RDP aka remote desktop you will have to open a different port number than ftp if you decide to use a firewall.
So in a nutshell, if you are trying to access your computer remotely you need to first install dynamic DNS or get a static ip address from your ISP. If you are trying to connect to your home computer in a local area network i.e. you brought your laptop home from work and you are connected to your home wifi, you can skip that step. Next you need to install a ftp server of some sort. I would recommend filezila, it's free and easy to setup. After you install filezila configure it by choosing the home directories for the user(s) that will be accessing it. Once that is done you most likely want to set up the username and password so not anyone can stroll in and take what they want from your computer. You also will want to set the permissions to control what they can do when they connect. Once your done on your home computer, you should be able to connect via ftp to retrieve files.