This can be achieved by using FaceTime and Screen Share through ➔ SharePlay. The content to share would be shared from the YouTube app. I have not tested this, however, basing my thoughts on the SharePlay feature.
This can get challenging when there are two iPads and a car is involved. It can get easy if both of the iPads can be used with FaceTime and have access to a cellular or a Wi-Fi Hotspot/Network. The other requirements is that both iPads must have iPadOS 15.1 or 15.2 installed. SharePlay was activated in iPadOS 15.1
Your iPad(s) Air 3rd generation can be updated to iPad 15.2.
If both iPads have access to Wi-Fi in your car then you can Pair one of the iPads to your car’s Bluetooth audio system and start the FaceTime Call to the other iPad. Begin SharePlay and use the YouTube video to share with the other iPad.
Axel F.