If you have any questions - just ask away. There are lots of ways in Hubitat to turn on a plug for a defined short pulse (like 100 ms or 200 ms) to simulate a button push. I did it by modifying a driver for the Peanut plug (a zigbee plug), but you could use rule machine.
There's also this collection of useful apps by @asj. One of them is called "when_on_then_off"; it does exactly what you would want for a GDO button.
