Can video recording be auto activated when camera app is started?
A custom widget ( start recording ) on your homescreen would work, but you still need to enter the PIN... 

Maybe a custom lock screen with a record video button and unlock button, or maybe use the stock lock screen shortcuts to open the camera, manually switch to video and start ( no PIN entry )   

The best way to do what you want might be to use key overrides and designate a volume key to camera key... 

Your main limitation is the lock screen PIN, you could hypothetically use a shortcut to the record video intent, placed on a custom lockscreen, but not sure.