In Missouri, a parent who has custody of a child cannot move more than 50 miles away from the other parent without getting permission from the court or the other parent. It seems like you have been proactive in seeking your ex's permission to move closer to your MIL and he has given you his consent multiple times. However, it's always better to have legal documentation to avoid any future disputes.
Your lawyer is right in advising you to send the certified letter, as it is required by Missouri law. Once the letter is sent, you cannot legally move for 60 days, giving your ex time to contest the move if he wishes to do so.
In terms of your ex's chances of winning if he does contest the move, it depends on the specific circumstances of your case and what the judge determines to be in the best interest of your child. It's possible that the judge may look favorably on your ex for being involved in your child's life and wanting to maintain a close relationship with them. However, if you can demonstrate that the move is in the best interest of your child and that your ex has given his consent, you may have a stronger case.
Overall, it's important to follow the legal process and ensure that you have all necessary documentation in place. It's also a good idea to continue communicating with your ex and trying to come to an agreement, as it's always better for both parents to be on the same page when it comes to their child's well-being.