I would not advise you to move out of state with the children without the agreement of your spouse. Your husband might decide to file in court for emergency custody and there is a good chance that the court might award him primary physical custody of the kids. As you may imagine, judges do not favor parents who decide on their own to remove children from the state.
If your spouse agrees to let you take the children to Michigan, then you MAY be able to file a lawsuit there for divorce, property distribution, alimony, child support etc. However, the courts in Michigan may decide that they do not have jurisdiction over your husband if he still lives in NC. Jurisdiction is a complicated concept, but it would depend on such facts as: (1) Did your husband have an active role in deciding the children would live in Michigan? (2) Does he own any property in Michigan? (3) Did he visit the children in Michigan and, if so, how often and where did he stay when he visited? From your post, it appears that your husband lacks any connection to the state of Michigan, in which case you may not be able to litigate against him there. If this is the case, you may find yourself living in Michigan while pursuing a lawsuit in North Carolina, which could prove difficult and costly.
Robin F. Verhoeven
Attorney at Law
Rosen Law Firm
4101 Lake Boone Trail, Suite 200
Raleigh, North Carolina 27607
The response posted above is based upon the limited factual information made available and is not intended as a full and complete response to the question. The only reliable manner to obtain complete and adequate legal advice is to consult with an attorney, fully explain your situation, and allow the attorney sufficient opportunity to research the applicable law and facts required to render an accurate opinion. The basic information provided above is intended as a public service but a full discussion with an attorney should be undertaken before taking any action.