Your situation is not only different; it's a bit unconventional. You cannot put two different outputs into one single input with a Y connector. You need some sort of switching mechanism. These things are not mics, they are Dots, an unless you want to blow one or more up and create howling, etc. It can't be done. Unless someone tells it can be, and then you will try it and likely blow things up anyway!
If you want a second Dot to ask it the weather, etc, just set up a second one in the same room, but it cannot control the other. That is sort of my situation with a Dot feeding a stereo, so I just ask the Echo or other Dot nearby.