I question if your Dots are really connected to the home network/internet. The Amazon XXX signal is a temporary signal we connect to during setup to be sure the Dot is connected to the phone, or Kindle, etc. You are then asked to return to your wi-fi settings of device using app for setup and select your home wi-fi signal your want the Dot connected to. If successful, app indicates so, and the AmazonXXX disappears for good.
Other than for the BT connection issue, do the Dots seem to work correctly?