You're going to have to specify a data directory to run from. When you switch computers, it is creating a new wallet and data directory on the machine.
To bypass this, you would create a Darkcoin config file specifying to use the data directory on the usb stick itself. Or edit the launcher with the following -datadirectory= usbdrive/.darkcoin
This is with any Bitcoin type coin though not just Darkcoin. For more help check out
https://darkcointalk.org