You tell her that you don't give permission and that if she relocates without your consent you will apply to court to have the child returned. I'm a bit concerned about your terminology... You said you have a binding child support agreement? Do you mean you have consent orders that stipulate the time you have with the child? A binding agreement pertains to money NOT child access - Child access is expressed in court orders / consent orders / parenting plan. The advice I'd give changes based on your answer.
this gets messy... WHAT IF? what if, she says OK, the kid can come live with you? Do you agree? IF yes then GREAT... If no, it gets messy.
With 4 nights a fortnight and half holidays, a court would be likely to refuse the move - however, relocation cases are the least predictable part of family law in my opinion. But I really would encourage you to write to the ex via text or email.. I'd write something like this.
Dear ex,
You have communicated a desire to move 8 hours away with XXXX. I do not give permission for this relocation. I will be relying upon this piece of communication in the event that I need to seek redress through the courts as a result that you choose to move with the child without court approval.
Basically, you are putting her on notice that you will not just let her go. Mate I've been in the same situation. I got letters from solicitors telling me that I should just accept it because the ex would take me to court and win... That got me a bit scared BUT it never went to court and the ex left the kids with me...