What you want it to do is then send another signal that trips a relay connected to the switch to reset the AC for you.

Yeah, I'd thought of that, too. And it's certainly an option. But the A/C is controlled by a battery-operated remote with rubber buttons that I don't want to mess up.

And we've already looked into problems with the remote as being the source of the issue, and it's not, as far as we can tell.