The second basic troubleshooting step:
Something could have gone wrong during the latest update procedure.
I would try to install a fresh copy of iOS. To do this, create a full backup of your iPhone (1), then restore it to factory settings (you need a computer to perform this step) and, in the end, set it up as new (2).
When done, restore data from your previously made backup (3).
Before executing step #3, please check your wife's iPhone and see if in Settings>General the Carplay option appears. Should be this case, proceed with step 3. If, after step 3, Carplay disappears, you need to check again ALL settings in that iPhone.
Follow the instructions provided in these support articles:
(1) How to back up your iPhone, iPad, and iPod touch – Apple Support
(2) Restore your iPhone, iPad, or iPod to factory settings – Apple Support
(3) Restore your iPhone, iPad, or iPod touch from a backup
If the issue still persists, contact Apple Support directly using this link:--> Get Support
Regards
Giulio