“But, he can’t travel out of state with my children without my permission…”

In Child Custody matters a parent can travel with their child during their time. And, NO, usually you do not need the other parent’s “permission.”
This is true whether you are the primary custodian or the visitation exerciser, there is no real, legal limitation on your ability to travel with your child.
You can run up to Gatlinburg, TN and see the Smokies, or you can head to New Orleans, LA to spend time in the Big Easy. You can hop down to Orange Beach, AL or Destin, FL for some fun-in-the-sun and there is not much the other parent can do about it…
Unless, there is a prohibition against such travel. Those prohibitions come in two forms, most commonly by agreement. This means the parties expressly agreed that their rights to travel with the children would be infringed. So, permission does have to be provided or the travel is limited to a geographic area or by travel time limits. Secondly, and less common, travel may be restricted by the Court. This is in the rare occasion where a parent makes a credible threat of leaving with the child or has done so in the past. If the Court Orders it, it must be abided by or there could be sever consequences.
The same holds true for international travel, though there are additional requirements, usually, beyond the Court. For instance, international travel would require a birth certificate or (passport which usually requires both parent’s consent.) Likewise, U.S. Customs recommends a child travelling with only one parent to have a written authorization for such. There may also be reasons to restrict travel based upon the destination and how that Country would treat a U.S. Custody Order.
Now, what is required is keeping the other parent reasonably informed. That includes travel, a means to communicate and it could also require more specific information, such as an itinerary, contact numbers for destinations, where you are staying and who else may be traveling. It all depends on your custody language in your Order.
So, can he travel? Yes. Do you have the right to know about it? Yes.
Matthew Thompson is a child custody lawyer in Mississippi and reminds you to be a reasonable parent and get out there and see the world. http://www.BowTieLawyer.MS (601)850-8000