That's not what a cell phone is.
You are talking about some kind of a separate communication system. Like a walkie talkie or something that works over broadcast. IP phones may be able to do something like that but you would somehow have to register the system to a single cell phone number, which wont work without a SIM card.
You could get two different phones and setup a google voice number to ring them both at the same time, first to answer gets the call.
Now that's an idea I didn't think of.
OP, why can't you just unplug it and take it with you when you go back and forth?