Like others, I’m a little confused about what part of the system isn’t working for you. But if you’re asking how you can use voice control to open and close the gocontrol garage door, as long as you have smartthings , it can definitely be done, but there’s a trick to it. So it’s not an intuitive set up, but each step is pretty straightforward and once you have the set up done it will work well.
What you would need to do is set up a virtual switch which the voice assistant Will turn on and off.
Then you will set up an automation in smartthings so that when the virtual switch turns on, the garage door will open; and when the virtual switch turns off, the garage door will close.
With Echo, you can choose any verbal phrase you want to initiate the switch turning on by using an Echo routine. And the same for turn off. So you don’t have to use the “turn on“ phrase if you don’t like it. I think there’s a similar facility in Google home, but to be honest I’m not sure.
In addition, I’m confused about why you would want to do this in your car if you already have a Homelink button. But if you have a reason for doing that, I don’t know how it works with Google assistant (there are some differences between that and google home) So I will leave that discussion for people more familiar with the Google side. There are some community members who have an echo dot in the car and do use it, so Choice is good. 
So there is some setup involved, but it can definitely be done, and each individual step is fairly straightforward.
One) create a virtual switch to represent the lock
Two) set up an automation so that that switch coming on tells smartthings to open the garage door
Three) fine-tune the trigger phrases in your virtual assistant. With echo, you do this with echo routines. I don’t know how to do it with Google, but I Believe there is a way
Four) if you intend to use this while you’re in the car, you need to set up whatever device you’re going to be using there to accept the verbal commands. I wasn’t quite clear from your post whether that’s your phone or not.
I’m going to leave any follow on discussion to people who are more familiar with Google, but that’s the general idea.