Can my Mom's husband take her out of state without my permission, if I have POA?

Having power of attorney doesn't let you stop your mom from doing what she wants to do unless she's been declared incompetent. Frankly, her husband is in a much stronger position than you are. As her husband, if she hasn't been put under your guardianship, he's the boss in this particular situation.

More info needed?

Do you have financial POA or medical POA? Does she have a healthcare proxy?