Legal Question in Family Law in Kentucky

Abandonment is not what needs to concern you. What you are describing, however, is grounds for modifcation of custody under Kentucky law and I suspect under other state laws as well. Further, if the original state with jurisdiction was Kentucky, you may be creating grounds for jurisdiction to be moved to Tennessee. The only way to do this with as little risk to the above as possible is to enter an agreed order in the court which specifies how these changes are to be treated in terms of modifying custody and changing jurisdiction. To accomplish that, you really should have a lawyer draft the agreed order.