You have the workings of doorbell 3 totally wrong. If it’s currently recording a motion detection it doesn’t alert to doorbell press. This is absolutely crazy. Doorbell press should take priority.
My doorbell will always detect motion before a press, as will most I guess. So don’t know if someone has rung the bell or not. They could be just putting a leaflet through the door.
Remember your basic function. It’s a DOORBELL first of all.