Hi Bo Duke
I was on a server you were on last night and you mentioned you had some probs then too
First there is a big difference between low FPS making the game appear to stutter and network lagg making cars jump about and dissapear alot.
I am betting your mums PC is connected via a wireless router is this the case?
Also when you say she has a "shared connection" who (how many) other users is it shared with? and are any of them using P2P programs or playing other multiplayer games?
Do a virus scan and run an anti spyware program as Franky said above.
if you connect via wireless could you try a patch cable? it should work alot better.
let us know all the info you can about other processes running on the PC maybe we can help you sort this out.
SD.