Just to chime in with my experience, I have a Kia Cee'd currently (waiting for my GTI to be built) and use Spotify on my iPhone 5s on the in-car nav/entertainment without issue (although it's not the full set of features). Obviously it's a different manufacturer but I think the way Bluetooth connects to mobile devices, it should send generic track control commands.
To get techie for a minute, all car stereos should use A2DP to get the audio from the device, and then use AVRCP to control the tracks, and assuming they do, these BT profiles certainly work on the Spotify iOS app as it works with other BT devices I have (headphones and home speakers).
I've found iPhone compatibility over BT varies between OS releases, so for example it worked fine in iOS 6 but was buggy in 6.1 and has been largely okay in iOS 7. Not sure if you guys are on the latest possible versions of the Spotify app and iOS on your phone, but as Spotify last updated on 27 Jan, you may not be possibly...
Anyway, here's hoping things either can be made to work or updates improve things, as I'm going to go nuts if I end up downgrading on my stereo with my GTI!

Also just to say jailbreaking isn't always an option as iOS 7 is tougher to break and the usual warnings about voiding warranties apply (Apple are a tight bunch and can tell if you've ever jailbroken your iOS device).