If you want to do it, be careful as it may erase the content of your iPod Touch when you plug it into the second computer. The trick is to set your iTunes/iPod options to manually manage your device.
To do this, connect your device to the second computer. Open iTunes. Depending on the setup, iTunes will most probably prompt you to Cancel, Erase and Sync, and Transfer Purchases. BE CAREFUL HERE: choose "Cancel".
Then, click your device in iTunes (left sidebar). Click the Summary tab. Scroll down to Options and click "Manually manage music and videos". That should do it.
For more details, read also this Apple Support page.