Tax law overrides a divorce decree. If the child does not live with the parent who claims the dependency, the other parent must provide form 8332 to the parent who is claiming the dependency.
I am not sure where to find the IRS rule that a child who qualifies to be claimed by a parent can't claim them self even if the parent doesn't claim them. If the parent doesn't claim them but could have and the child claims them self, it's not likely that the IRS would challenge it.
