If management wants to fire Babcock, they will have to go to George Cope and Joe Natale, and they will decide.If Management wants to change the Head Coach, they will do it by asking Babcock to take another job in the organization.
If he refuses, and wants to continue coaching in the NHL, he'll have to resign his position, otherwise he sits.
Well, that's if there is no protection against this in his contract!
A team that is owned by two publically traded companies, cannot fire an employee who is owed 30 million without strong reason. They don't give that power to two people who make less than him unilaterally.