What can be done in Missouri if you have joint custody that states you have to give a two-month notice before you move and she gives you two weeks' notice that she's moving out of state with kids?

It doesn't really matter where you live, the law speaks and she has no business doing this. Please seek out a lawyer and fight it. If she has to move because of a career move the odds may not be in your favor, but the judge will make other arrangements and you may get to see your children every second month or holidays. Usually the husband is entitled to have the children during the summer holidays and Christmas holidays are usually alternated from year-to-year. Good luck Marcy