How can I use different magic mouses at home and at work?
Afaik what happens to you is not default OS X behavior. It should always connect to any input-device that is nearby automatically. 

You could try the following:


Remove all bluetooth devices from the bluetooth preferences
Delete com.Apple.Bluetooth.plist from /Library/Preferences and/or ~/Library/Preferences (once I had it in both... not sure why)
Reboot
Pair devices again
Reset your PRAM by holding ⌘ Command+⌥ Option+P+R after pressing the power button when turned off. Hold it until the startup-chime is heard for the 2nd time.