What you would need to do is to setup a logic analyser on the physical interface between the computer and dongle. For example if it connects to the serial port then you could use a small piece of Veroboard with a serial plug and socket mounted at each end, and a header between the two. Plug the board into the PC and the dongle into the board, and your logic analyser into the headers. By analysing the signals over time you will be able to design hardware to replicate the behaviour, which you might be able to do with a low cost bit of hardware like a PIC chip.
Code:
------+ Veroboard
| +------------+ +--------+
PC |==| oo |==| |
serial|==| oo |==| dongle |
port |==| oo |==| |
|==| oo |==| |
| +------------+ +--------+
------+ header
pins
Alternatively just borrow the dongle whenever you need to use the software. The point of the dongle is to prevent software piracy, and for multiple licences to be used at the same time you will need multiple dongles. If you can justify the use of the software then your employer may be able to get a licence (and therefore a dongle) for you to use.
Also check out the software licencing arrangements. Maybe there's a restricted "training" version that doesn't need the dongle and might be enough for your home needs.
