Smart trainer connecting to Garmin in cardio activity

Hi there

I have a Garmin Fenix 6 Sapphire, and my fiance has a Garmin Forerunner 745. Both of us use a smart trainer (Wahoo Kickr) to train sometimes and record it using our watches with no problem.

However, we do have a problem - when I ride the trainer (connected to my watch) and she exercises next to me using the Cardio activity on her watch, her watch connects to the trainer and records my power output.

Is there a way to disassociate the smart trainer accessory with the Cardio activity? We want to keep the smart trainer on her watch as we don't want to keep disconnecting and connecting it every time she wants to ride indoors. All we want is for the watch to not try to connect to the trainer using the Cardio activity.

Thanks!