I believe the norm is to have it addressed in the courts when the other moves and needed a modification of the child custody order to legally accomplish this.
Other than that, unles you have a court order mandating your financial participation, you have no legal liability to pay anything.
Often, those in the know on this forum often state it is typically the parent that moved to pay for the addidtioanl expenses incurred due to their move. Why should you pay for their actions?