Would my ex-husband be able to bar me from doing this since in my mind that is in the best interest for my children and us?

More information would be needed. How far would you be moving, what are the ages of the children, what is the parenting schedule for the "ex", how flexible is this person. Minimally, you may want to seek a consult with an experienced family law attorney regarding your plans, and perhaps a counselor, but it depends on the full circumstances. Generally, though, it is often difficult to relocate absent a compelling reason, if it means that it will cause the other parent to lose substantial or meaningful parenting time.