I’m getting clearer picture of your use case.
Your current doorbell pro will only bind to its own chime.
I’m not aware of a solution not using the house wiring. You would have to get an appropriate plug in power supply, run wires, etc.
The doorbell v2 may have a solution. There is a support note that details how to accomplish a front/rear setup.
If I understand this you would put the v2 on the front door and leave the back as is. You would also need another chime controller.