One iPhone connected to left AirPod and another iPhone to the right AirPod.

No this is not a common thing! Have you tried to reset the AirPods to factory settigns to see if the issues persist?

1. Put your AirPods in their charging case and close the lid.
2. Wait 30 seconds.
3. Open the lid of your charging case, and put your AirPods in your ears.
4. Go to Settings > Bluetooth. Or go to Settings > [your AirPods].

• • If your AirPods appear there as connected, tap the More Info button next to your AirPods, tap Forget This Device, then tap again to confirm.
  • If your AirPods don't appear there, continue to the next step. 

1. Put your AirPods in their charging case, and keep the lid open. 
2. Press and hold the setup button on the back of the case for about 15 seconds, until the status light on the front of the case flashes amber, then white.*
3. Reconnect your AirPods: With your AirPods in their charging case and the lid open, place your AirPods close to your iPhone or iPad. Follow the steps on your device's screen.