I guess the next steps depend a bit on how much you're prepared to annoy your visitors and/or your dogs in the name of Science. If you cut power to the whole system, do the dogs still go bananas? (Are they hearing the physical noise of the button-press?) If you disconnect the chimer's speaker leaving the button live (if that's possible), do they do it? (Does the chimer make some high-frequency coil whine or suchlike that they're hearing?) Assuming the button is "dumb" (momentary, normally-open), if you briefly short the wires at the chimer end (simulating a button-press) do the dogs react? (If you're that close to the chimer when it goes off, maybe *you* will hear the coil whine.)

Peter