The issue you are experiencing likely has nothing to do with the VPN. Network connectivity is not needed to unlock the car. I have been in places with no cell phone signal and it still works.
I do sometimes experience the same issue you are. If I wake up my phone, then it works. So it may be working for you not because you disabled the VPN, but because you woke up your phone and it then sent out the bluetooth signal to let the car know you were nearby.