You can't share with a remote network using Homegroups. It will only work on the LAN and also won't work in a domain.
Even if connected to a Homegroup locally you have to create extra User accounts on each machine in order for the User names to appear on the "share with" list. If you don't do that you will only be able to share with Everyone or Nobody.
There is a process for doing this but it's not easy, I can post it if you want me too.
If you need to share files with a remote machine try Team Viewer which needs to be installed on both machines.