Please see previous response.
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Mr. Scholl already answered as far as leaving the state. I want to address your "no fault" issue. There is no "no fault" divorce in arkansas. The only ground that doesn't involve fault is separation for at least 18 months prior to filing, but that is not available to you since your question says you still live together. To get divorced, the one who files must show the other party is at fault. There are specifically delineated grounds for divorce in Arkansas and you must meet one of those. You should talk to a family law attorney to learn your rights and obligations.
No attorney-client relationship is established with this answer. It is not to be considered legal advice, but is merely given to point you in the right direction and give you a general answer as to the law regarding the question you have asked.
Your question raises several points. First of all, there is no such thing as a "no fault" divorce in Arkansas. You must have grounds for divorce. Secondly, both you and your husband have equal right or authority over your children until you have filed for divorce. That means either one of you can take the children out of state. However, once you have filed for divorce there is a standing order that goes into effect that may effect whether you can take the children out of state. Standing orders vary by county, so you need to consult a family law attorney who practices in your county. And finally, you cannot get a divorce in Arkansas unless you are a resident at the time of filing. And if you wait to file until after you move, you will have to live in your new state for a bit to establish jurisdiction. When children are involved, the children must reside in the new state for six months before that state has jurisdiction. Your situation has the potential for some problems so you need to talk to an experienced family law attorney.