My healer Chocobo stays put once it starts attacking in "Free Mode". If I need to re-position it, I have to move to where I want it, hit "Follow Mode", then hit "Free Mode" again to plant it there. The same has to be done to switch it's target. I just have to attack the new target before I switch my Chocobo back to "Free Mode".

Chocobos are just one of many great ideas in FFXIV that was poorly implemented and then ignored. I'm really hoping to see some improvements on some of the original broken content soon. SE has apparently been too focused on adding additional (broken) content instead though.