I am afraid I am firmly on the fence here, my child advocate side says it sounds like a great situation to allow her some freedom and you know your dd well enough to know if she is sensible etc.
However, my paronoid, aliens may come from the sky, side screams that is it a terrible risk.
TBH, I think I would come down on your side overall, however I can see why ex and dm reacted the way they did IYSWIM.