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DearCustomer- Well it's neither abandonment or kidnapping in the case of a 17 year old. Virtually every court will approve of the move if the child wants to live with the other parent so there is really nothing to argue about.
If the mother wants to amend the child support she will have to do so through the courts. You can simply do nothing and the support will stay the same until the mother files for a change of custody. At that point the child support will be adjusted.
You really don't have to file anything and if the mother files for the change you would be wasting your time to object. In less than a year your daughter will be and adult and can do whatever she pleases so getting involved in a court battle at this point makes no sense.