Anyway I can just make the whole second HDD a shadow of the first one
In the simplest terms. Raid1 Its the thing I think you are looking for. Its a simple mirror system. Drive 1 and Drive 2 are exact copies of each other.
However if you are using your drives as sharing of media, I would suggest setup of a NAS(Network attached Storage) drive. its a drive that can connect directly to your router and then you can share it across your entire network. The benefit of this, is your computer doesn't have to be on to share anything and generally speaking NAS drives are designed to be a bit more robust. Less prone to failure.
You can get simple ones that are around the same cost as a new HD or you can get into the $$$$ with them. Some versions already have multiple drive setups with raid configurations.
The other upside to this is you can setup a folder on your local Ubuntu machine that "looks" local to your software, but runs on the share.
Example. On my machine i have a /media/plex/tvshows folder that actually sits on a NAS drive. This allows me to save all my shows there without having to worry about filling up my Computers HD.