In a modification hearing because of a relocation, the judge will be looking for two things: (1) that a substantial change in circumstances affecting the wellbeing of the children has occurred, and (2) that changing the custody order will be in the best interests of the children. If both of these cannot be proven, then the judge will not grant a motion to modify the court order.
You should focus your case on why the relocation is beneficial to the children and in their best interests. For example, a relocation could provide better schools or there could be more educational and cultural opportunities. A relocation because of a change in jobs could mean that you are able to spend more time with the children or allow you to better financially provide for them. Or, a relocation could remove the children from a dangerous, harmful or unhealthy environment.