Hey!
There's no way to integrate Spotify to the game as far as I know.
The way I use Spotify while I drive is that I put playlist I like playing and then go back into the game. My keyboard has Fn keys, so I can skip songs and control volume while Spotify stays on the background.
Another thing you can do is that you use another device to control Spotify. It can be laptop, phone, tablet or anything you can install Spotify on. When you login on the same Spotify account on the device as on your computer, you can control Spotify via that device while your computer is the device playing the music. You can basically do everything: skip songs, change playlists, control volume, queue songs etc. Everything that you can do on Spotify on your computer.
I do not know, if what I just described is Spotify Premium feature, so you'll have to check it for yourself, unless you have Premium. I hope I could help!
Regards,
Ampelmann