Does the software license allow the same license key to be installed on 2 computers? The two computers will never be in use at the the same time, I want to access the lan via my PC when I'm at home, and also via a laptop when I'm on the road.

No, you can not install the same software on another computer. Once the software is activated, it will not allow you to use the software on another computer for more than 30 days.

You will need separate license and you will need to activate them seperately.