Its not a Vista specific issue the Internet being slow for a VPN user, more of a "by design" issue.
When the user is VPN`d in, the VPN network becomes the default gateway for the computer, and so all Internet traffic is going through the VPN, which is obviously much slower than directly to and from the local computer via the local cable connection (usually it is the upload speed on the VPN end point that is the cause of the slowness, as this becomes the download speed of the local computers internet connection).
Depending on the type of VPN (Windows built in, Cisco, Netgear etc), you can usually configure it to not use the VPN connection as the default gateway, however this does of course bring about some potential issues with the local computer creating an unprotected bridge between the internet and VPN endpoint. As long as you understand those risks, it is safe to change the default config of the VPN.
(Hmmm, just read that back, not my best explanation!!)
In addition to above... (excuse me if terminology/info is not perfect)
If User is connecting via VPN, then the VPN software creates a "tunnel" over the internet (through the Users (ISP's) internet connection), to an endpoint (e.g. usually your works LAN).
To get back out to the internet, the Users system will probably then use your work proxy server. Which then due to the additonal hops (e.g. Computer -> ISP -> internet -> vpn -> work LAN -> proxy server -> internet), and load / speed of your works proxy server / LAN, will show a slow down the Users internet access speeds.
Also, as VPN's are normally used for work/corporate use, I've heard that some ISP's limit the speed that they allow VPN's to connect through their routers/network at.
Re the shutdown issue, advise the User to disconnect their VPN connection and then shutdown their VPN software before trying to shutdown windows. (Part of the windows shutdown process is to close open network connections.) If the User doesn't remember to do this then you can enable a shutdown script (via group policy) to kill running apps / services.
Something (e.g. application / service) may be stopping Windows from shutting down, so try and identify what that may be (look at Event Logs after shutdown attempt, look at Task Manager to see what's running).
Or try registry hacks like... (I do not validate these, do your own backup & testing first!)