Now I want to be able to create two separate objects, which aren't connected with wires, to be able to talk to each other.
Hmm, that sounds like this newfangled "wireless" stuff. 
Off the top of my head, I would guess that Xbee would be a decent compromise between cost and usability, although I don't know how easy it is to work with on the Arduino.
Bluetooth would work but is expensive. Dumb RF modules would be cheap but tough to code (and maybe build, especially with >2 units).
GPS won't work (reliably, accurately) indoors, and 20cm is way too much resolution to expect from GPS, even outdoors. That may even be too much to expect with a differential GPS setup, but DGPS is probably beyond the scope of a teddy bear project.
Not sure if Xbee has RSSI (received signal strength indicator). That could be useful in determining distance.
Maybe the Nordic wireless comm stuff would work? I haven't dealt with those, either, although IIRC there is some Arduino code for them out there.
-j