If you look at the properties for the shared internet connection (the modem), under advanced you should see options for "Establish a dial-up connection whenever a computer on my network attempts to access the internet" and "Allow other network users to control or disable this networl connection".
You could try un-ticking these which may stop the problem. You may also need to select never dial when a connection is not present.
Whilst this may stop the problem it`s not very satisfactory as the networked PC and possibly the main one will require you to manually establish the dial-up connection before you can go online.
The usual reason for this is software that attempts to "phone home".
Your anti-virus software for example may be set to check for updates whenever an internet connection is present - which as far as it knows is always the case when the LAN is connected.
Even if you re-configure every piece of software you can find you`ll still get the problem as Microsoft seems to require Windows to "check in" whenever it gets the chance.
Hopefully someone else may post a better solution?