According to the Trillian manual Installation section, you can install the large library files on the HD of your choice:
However, the System Requirements seem to suggest that you have to have at least 70GB free on the startup drive for the installation (not clear if that applies even if the files are to be installed to a different HD), so you should research that carefully (and check with Spectrasonics) before proceeding with the download.
The FAQ also says that you must install the entire library, and I think it said it was around 35 GB or so. But remember, you really want (need) to keep 20% of your internal HD space *empty at all times*.
As to the CPU spec, a dual-core CPU is on the weak side for any DAW/audio application these days. I'm sure it'll run, but the question is how well, and that will also depend on how much RAM you have (8GB minimum, 16GB recommended), and how many other VIs you're running simultaneously. If they have a demo version with a small library install I'd recommend trying it out first to make sure that your computer's spec will be enough.