Apps won't update: "not enough space"

She has a 2nd generation 8GB iPod Touch as they never made a 3rd generation 8GB model.

Try Restarting and Resetting...

I would also advise you to take a look at and read the iPod Touch User Guide.
http://support.apple.com/manuals/#ipodtouch

It explains how to Restart, Reset, Restore........

1. *Restart iPod touch:* Press and hold the On/Off Sleep/Wake button until the red slider appears. Slide your finger across the slider to turn off iPod touch. To turn iPod touch back on, press and hold the On/Off Sleep/Wake button until the Apple logo appears.
If you can’t turn off iPod touch or if the problem continues, you may need to reset iPod touch. A reset should be done only if turning iPod touch off and on doesn’t resolve the problem.

2. *Reset iPod touch:* Press and hold both the On/Off Sleep/Wake button and the Home button for at least ten seconds, until the Apple logo appears.
For more troubleshooting suggestions, see Appendix B, “Support and Other Information,” on page 214.

And More..........

Then keep reading the Users Guide....

Restore or Restore as new.....
Make sure she has everything backed up when doing the above as it may erase everything.

Let us know.