I have the same hardware setup as yours but I use IFTTT to link Google Home to Broadlink. IFTTT can accept the voice commands recognized by Google Home and issue webhook request to your HASS to trigger a script. The script then do what you want it to do like toggle switch twice and turn on other device afterwards. So the execution flow as this one:
User speaks voice command -> GH recognized and sent it to IFTTT -> if IFTTT found pre-defined applets match the command then send webhook request to trigger script, otherwise no response -> HASS get the request and then execute script.
emulated_hue plays as IFTTT but is not so flexible. The problem of IFTTT is that you have to create as many applets as the voice commands you need. Applets of IFTTT are edited with web interface which is user-friendly but not efficient if you want to create tens of applets.
The alternative way is to use Google API.AI which also can send webhook request. It can replace IFTTT with more flexibility on voice commands (use intent instead) and can create more human-like responses. The trouble is that you will need some time to learn API.AI and it is always in test mode unless you publish it.
I have tried both and now use IFTTT. It is because the setup is easy and I just wan to have 10~20 commands to control home devices. IFTTT is enough for my purpose.