If you want to move with the children or you are afraid that the other parent wants to move away with the children, it would be best for you to compile a list of reasons why the move would be beneficial or detrimental to the children, depending on your motive. These cases can be complex and the laws concerning these topics are ever-changing to it's best to seek the advice of a professional.
Often if a parent who has sole or primary custody of the children they are able to move unless the other parent can prove to the court that the move would harm the children. Likewise if the parents have joint custody and one parent does not want the other to move with the children, each must prove to the court why the move would be good/bad for the children.
Even if you have a parenting schedule in your child custody agreement, the judge will often look at the actual schedule around the time of the move to before making a decision. If you are worried that the other parent might abduct the children, you need to speak with a lawyer to come up with a plan to best protect your rights and your children.