You put the 2 TB drive somewhere else (at a relative's) and keep it updated regularly via network.
That's my set up (but with a bigger drive).
At home, I have the master copy of the data on my file server. Then I have backup #1 that is in the same location and backup #2 that is in a different location.
Both #1 and #2 get updated at night with a "timemachine-like" backup system based on rsnapshot. The network traffic goes over ssh.
Remote backup system #2 cost a UPS, a RaspberryPi and an 8 TB drive, which is about ~$250-$300 total.
The initial sync is best done locally of course, but deltas can generally easily go over network at night.
Cheap, reliable, and (relatively) easy (if you're a geek, that is).