The music is on your computer, but you want to try accessing it from her computer? Currently, iTunes does not support that functionality. However, if you ask KnifeMissle really nicely he might be able to program something that will allow remote access of music in iTunes
See this thread -
http://www.tfproject.org/tfp/showthread.php?t=112587
You may be better off just burning everything to a CD or an external hard drive and taking it along with you. If you were able to network your computers together then you can listen to your music on her computer, but thats about it. No file transfer.
Sync ipod with 5 computers = I think this is only for music purchased from iTunes, not mp3s or anything else.
You can hook up your new ipod to her computer, and it will ask if you want to sync it with her computer. She can then put her current one back in after you unplug it and it should continue to work normally.