One common misconception among separated or divorced parents is that you always need your ex's permission to take your child out of state. This isn't necessarily the case. It depends on the status of your marriage.
If the Papers Require Permission
Child custody law is governed by state law. If your state's child custody laws are silent – they don’t say anything one way or the other about taking your child out of state without the other parent's permission – you're generally still prevented from doing so if your court order or parenting agreement says that you'll only do it with your ex's knowledge and consent. Sometimes you have to agree to such provisions to settle the case, or the judge might have ordered it for some reason, such as because at least one parent's past behavior indicates that it's necessary.
If There Is No Order or Written Agreement
If you have no written order or parenting plan agreement in place, you're generally free to take your child out of state for short periods of time as long as it doesn't interfere with the regular custody schedule you've established. But keep in mind that there's a difference between whether you can do something and whether you should. Unilateral activity like flying to the other side of the country and staying there for two straight weeks could so infuriate the other parent that you might find yourself in court. You'll have a court order before you know it, and it will probably prohibit such actions. Doing things without the other parent's consent or knowledge can make you appear uncooperative and controlling.
The opportunity to take your child out of state for a vacation or a visit with extended family may arise at the beginning of an ongoing litigation before any temporary orders are put in place. Although you might not be legally prohibited from doing so, it's often a good idea to refrain from going against the other parent's wishes, at least without your lawyer's advice. If your request is reasonable and the other parent withholds consent, this might make her appear spiteful and controlling in the eyes of the judge when and if your case goes to trial. A refusal might ruin your vacation plans, but it can become a valuable tool in court.
Taking the Child Out of State Permanently
Although you might be able to temporarily take your child out of state without the other parent's consent, you almost certainly can't get away with doing it permanently. Unless you live on a state's border and you're moving only a few miles across the line, your decision will have a serious and permanent impact on your child's relationship with his other parent. The move may be good for you and it may improve your child's quality of life, but doing it without the other party's consent and the express permission of a judge can endanger your right to custody. Moving your child out of state for good almost invariably requires a relocation trial if your child's other parent isn't in agreement, and it's possible that the judge can order your child home again until the matter is resolved.