I say, buy some quality surround sound speakers and let the pets get used to it. That's what I did with all my dogs. But then audiophile quality sound reproduction was my first love in consumer electronics before I got into computer way back in the 70s. So I might be a bit biased!
Otherwise, you are right and Windows only wants to see 1 device at a time (and still have both remain in sync with the audio source). You might consider something like an external audio receiver via the Line Out from your computer and a splitter to two headsets. The problem there is volume. If you connect two headsets in parallel via a splitter (on the receiver or your computer's sound ports), the volume to both will be greatly decreased. And most audio devices will not allow you to turn up the gain (volume) too much because they (the device makers, or rather their shysters) don't want to get sued for bursting eardrums. And the headsets would have be identical or else one set would be louder than the other. And also, when you put two loads (resistance) in parallel, total resistance (the load on the amps) actually goes down. And Ohm's Law dictates that when resistance goes down, current goes up. And when current goes up, so does heat - which is then hard on the amp.
So headsets/speakers via a splitter is not a good idea anyway you look at it.
Depending on your sound device, you can sometimes turn the Mic input jack into an output jack. In that event, you can indeed use two headsets (or one headset and one set of speakers). Adjusting volumes to a comfortable level for each set may still be an issue but worth checking out. See
this and good luck.
And back to the pets, they really do get used to it pretty quick, unless you have a monster sub-woofer rattling all the windows and knickknacks on the shelves!
