If an added antenna wire extends the range just enough for the unit to work, that would be OK with me and my neighbor, I think. I just haven't been able to figure out where the antenna is on the doorbell button unit!
Well, at least she's got a constant problem - it doesn't work/not work. It doesn't work at all anymore at the range it used to.
To be most effective as a "Faraday cage" I assume it should be grounded, but I also think the RF output of the router would be seriously attenuated by the pot, grounded or not. With her understandable reluctance to shut down the router, it's going to be hard to "indict" it as the cause. I recommended that she relocate the chime's base unit to be much closer to the doorbell unit than it is now. Right now, we've relocated the doorbell switch to the center of the wooden front door, behind the storm door and it works from there. Still, she would rather have it along the edge of the doorframe but it doesn't work there. She may be better off with the "inside the storm door" mounting arrangement because the last switch got wet and corroded and the tiny microswitch has failed.
I told her I could fix the corroded switch by wiring it to an alarm contact so that if anyone opens the storm door, the unit will fire. She liked that idea. Attaching the doorbell switch to alarm contacts has another benefit. I can locate the "guts" of the doorbell switch inside the house and much closer to the base unit. In fact, I can take a garden variety hard-wired doorbell button and mount it outside and lead the wire inside to one of her spare RF doorbell buttons. I'd do that by unsoldering the bad/corroded tiny pushbutton switch from the circuit board and then soldering wires from the hard-wired doorbell switch outside to the spots on the board where the old switch was soldered. That would mean that the RF transmitter was now inside the house, protected from the weather and closer to the base unit.
All in all, it's probably going to be cheaper and easier just to get a better/different unit.
-- Bobby G.