thinking out loud here…
You may find it easier to put a relay or opto across the local button if it exists,,or dedicate a remote to the task, and ‘press the button’ remotely…across a 433 or similar remote radio link.
- or maybe you could boost the performance of the existing receivers with a better antenna, or simple RF amplifier.
I’m guessing it’s only one-way communication, so the rx antenna might be the easiest answer.