Cole Tierney said
Another idea would be to get an inexpensive router to handle multiple internet connections. I'm not suggesting this would solve your problem, but it might.
I strongly agree with Cole Tierney about getting a router and not using your Mac mini Internet Sharing.
While Internet Share is useful in a pinch, it is poor substitute for a real router.
First of all the WiFi encryption is WEP with can be cracked in under a minute.
If you have Macs WEP can use character passwords, but if you have PCs or Linux boxes, you will have to get the hexidecimal equivalent value and use that on the PCs and Linux boxes. Very annoying.
Because your Mac mini will be on the subnet created by your ISP assigned IP address, which will be different from the subnet created by Internet Sharing, it maybe difficult to actually use file sharing with your Mac mini. You mileage may vary.
A router between your ISP and your Mac mini would give you a hardware firewall. Directly attaching your Mac mini to the ISP's broadband modem means your Mac mini is exposed to all the dangers of the internet.
As for connecting/disconnecting to the ISP's broadband modem, you could do the following:
System Preferences -> Network -> Location -> Edit Locations
Create a new location and name it "WWAN Off-line"
On the side-bar of network interfaces for this new location
select the interface used to talk to the broadband modem
Click on the gear at the bottom of the side-bar
and select "Make Service Inactive"
"Apply" your changes.
Now create a script that uses the scselect command (man scselect)
#!/usr/bin/env bash
/usr/sbin/scselect "WWAN Off-line"
sleep 5 # sleep for as long as you need to
/usr/sbin/scselect "What Was You Normal Location"
Since the "WWAN Off-Line" network location has disabled the interface (I assume ethernet) which talks to the broadband modem, that should break your connection.
Which you switch back to your normal network location, the interface that talks to the broadband modem should become active and re-establish a connection to your ISP.
Not sure if this will work for you, but I think you would be better getting a router. They are not expensive. They generally are WiFi base stations as well, frequently come with extra ethernet ports, some will host a printer or a shared disk drive. If cost is a factor, try searching over at <http://dealmac.com> and you should find some very cheap WiFi Routers.