Can my wife take my kids to a different state if I'm charged with domestic violence in Michigan?

If charged with domestic violence, there will be a no-contact order in place on day one.  Assuming we can remove than you would be able to return home.  During this time as long as your kids were not alleged victims of violence, there are no restrictions against seeing them or talking to them.

The above question would be more relevant if the DV charges were followed by a divorce or a custody filing with the family court.  This assume the other parent wants to move to another state than where they currently reside against your wishes.  Parents can take kids to different states temporarily and if both parents want to move then sure, anyone can change states, but if you are against this move, what's the likely outcome. This is called change of domicile.

Michigan law prohibits a parent of a child in a joint custody arrangement in Michigan from moving more than 100 miles away from the child's legal residence at the time the custody order was issued.   There are exceptions in Michigan cases such as the other parent agreeing or if the original residence was initially 100 or more miles away, and this move actually brings the child closer.

Yes, but an award concerning child support, custody and parenting time in Michigan is always subject to the review by a Michigan court, and can be vacated if the judge finds that the award is not in the best interest of the child.  A few things to consider.  

First, is there a current custody order or judgment in place?

a. If yes, then the domicile or residence of the child/children may not be moved from Michigan without the approval of the court where the order or judgment was entered. In petitioning the court for a change of domicile, you must show proper cause or a change of circumstances.

Unless any of the following exceptions apply under MCL 722.31(2)-(3):
i. The relocating parent has been granted sole legal custody;
ii. The parents’ residences were more than 100 miles apart when the legal action commenced;
iii. The move results in the residences being closer; or
iv. Both parents consent to the residence change. (Such consent must be as to a specific relocation and not one provided in general terms prior to a relocation plan.)

b. If no: 
i. Will the non-relocating parent object?  
1. If yes, will the move change the child's Established Custodial Environment?
2. If no, obtain consent in writing (e-mail, text, print, etc.) and GO!