Maybe. Barring some kind of restraining order or state law to the contrary, either parent can move and take the children with them. However, you probably won't be able to file for divorce in the new state right away. In order to obtain a divorce in a state, you must satisfy the requirements for residency in that state (typically living in that state for three to 12 months). Even after you satisfy those requirements, the state may grant you a divorce but have no jurisdiction to decide the other issues of your divorce (like property division, support and custody), because there may not be personal jurisdiction over your former spouse, because he or she is in another state. And while you're living in the new state waiting for the residency requirement to be met, your spouse can file in the state where you lived before, forcing you to travel there to defend yourself in the divorce proceeding.
The states recognized long ago that a parent might take the kids and move across the country in order to make things more difficult for the other parent. The laws are generally written to avoid that possibility. It's best to consult with a local attorney before moving.
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