Ok, sounds like I should just forget the software solution and stick with using two computers. I'm only going to be playing two accounts.
I'm not sure where you drew that conclusion from - playing two accounts on a single machine is a very efficient way to play

Yes, most of the software solutions - including Keyclone - work on both single and multiple hosts.

Have a look at the Wiki and the Software Tools forum - there's a precis of each option there, and it'll only take you a few minutes to get an understanding of the strengths and weaknesses of each.

If you go with Keyclone, and stick to two machines, be aware that you need two licences - one per machine.