Under the UCCJEA MS is going to have jurisdiction over any children unless you wait to file until they have been here long enough for NH to become their home state (6 months). You should speak with a local attorney who can review the facts of your case and determine whether it is better to try to proceed now in MS or wait until you can file here.
I agree with Anna regarding custody. However, there may be a way to get the case moving forward in New Hampshire depending on whether or not you have children. I would take a look at the divorce statute, RSA 458. A link to the statute is below.
Feel free to call me for a consultation as well. I work in the Dover/Rochester area. My office number is 603-865-1918.
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