Thank you very much for your contact.
Indeed, best practice would be that only the Ping sensor triggers a notification and all other sensors of this device, in this case the client, are paused. This can be done with configuring Dependencies properly.
The easiest approach would be to open the Settings tab of the Ping sensor and scroll down to Schedules, Dependencies, and Maintenance Window. Disable the inheritance and select the Dependency Type to Master object for parent.
Save your changes afterwards. This will set the Ping sensor to be the master object for the parent device. If the Ping sensor fails (is down) all other sensors will be paused automatically. If the Ping sensor is up again, the paused sensors will be started automatically.