Funny thing about that. My car theoretically should have been able to receive text notifications and never did. Until after one of the IOS 11 upgrades. After that I started receiving imessage notifications. I don't think notification forwarding was ever enabled until recently on iphones. Try this, go into Bluetooth settings while you phone is connected and look at the properties and see if notification forwarding is enabled.
If that doesn't work, download the ios 11.3b2 public beta. It's actually pretty good on my 6s and maybe will resolve your issue.