I can connect my QC35-2's to my phone and to my pc independently and simultaneaously, but if I use the Connect App on the phone, I cannot connect to the PC. In fact, if the app is running on my phone it directly prohibits re-connection to the PC. If I install the app with the QCs connected to both the phone and the PC, it registers as connected to both devices, but if I turn off the QCs or diconnect the PC via the bluetooth connections portion of the app, the PC will non longer connect. As I said, BOTH devices connect fine WITHOUT the app, but the "connect" app does eveything but.
That's a really interesting issue. Thanks for all of the details you've provided. So I'm thinking we should start with clearing the pairing list on the headphones. To clear the list you'll slide and hold the power switch all the way to the right towards the Bluetooth symbol and hold it there for 10 seconds, you should hear a voice prompt letting you know that it's cleared. At this point make sure to delete the headphones from both of your device's paired lists. At this point, you can reestablish the connection.
I would also recommend trying deleting the Connect app and reinstalling it. Let me know how it goes?