I currently live in MO. My divorce occurred in MI and my children's father still lives there. I am considering a move to Mexico with my new husband and my two children 7 & 11. I have full physical custody, but my ex has joint legal custody. Looking for any help and advise, maybe similar situations.

You have to file in the court that issued the decree for permission to move.

Since your ex has allowed you to move out of state already, the only issue will be making sure he has ability to visit the kids, the same as he does already.