I am going to guess that what you are saying is the horse moving collected "one her own" is probably the horse moving tense or braced. Do you mean that it carries its' head high in the air? Or that it comes behind the bit, even if you hardly put any touch on it at all?
How would you describe this "collected" way of going? Are the steps really short and "pronky" , like a gazelle? Is the speed fast, such that the horse feels like they are rushing in order to not fall forward onto their own nose?
Does any of this ring a bell or make sense to your situation?