It sounds like you are going to have both the AIU and pushbutton operate in parallel, so either the pushbutton or the AIU handheld could be used to operate the uncoupler.
This is how I wired my fastrack uncouplers, and it works OK. I found that the AUX power to the uncoupler had to be about 13+VAC in order to work on some of the stiffer rail cars. Some cars require more power to make the uncoupler work, while others (generally the newer cars) require less power. I use a Lionel 1033 transformer fixed voltage posts which are supposed to deliver 16VAC, but the volt meter measures only 13.9VAC. this is enough to operate my uncouplers properly.
I use a terminal strip at the AIU to simplify my wiring. I have The AUX power connect to the terminal strip, then use a jumper wire to create a number of powered connections on the terminal strip for each uncoupler I have operating on the AIU (in my case I have 6 to 10 uncouplers connected to each AIU. You can then connect the pushbutton to the terminal strip input side, and have a pair of wires going from the terminal strip to the AIU. In the picture below, the uncoupler terminal strips are on the top, and the switch terminal strips are on the side of the AIU. There can be multiple wires on the input (top) side of the terminal strip, and a pair of wires going from the terminal strip lower part to each AIU ACC port. (in the picture below, the ACC ports are connected, buy the SW ports are not yet connected)
An option I use when the AIU is far from the uncoupler, is to wire the uncoupler to the uncoupler track (normal method), using the AUX power connection (not the track power connection), then run a wire pair from the uncoupler track to the AIU. this requires crimping 2 wires to a common connecting pin, so the AIU wire and the pushbutton wires are both connected to the fastrack connection pin.
Hope this helps: Joe K