Revoking the other custodial parent from claiming a dependent

I am divorced with 4 kiddos, we have joint physical and joint legal custody of them. In some cases my sons have not been going to their dads for visitation so therefore they have lived with me the majority of the year. I was under impression I could send form 8332 certified mail to the father revoking his right to claim them since they lived with me. Is this correct? I am seeing custodial and non custodial verbiage and we are both custodial by what I’m reading in our decree. Is this form valid then to send or not? If ever audited how do u show the child lived with one parent more than the other? Want to make sure I'm filing correctly to the IRS because I had sent that form to him to revoke one of my boys since he was not going there to be with other parent.