Having trouble following this. Can you show a few images or a video perhaps?
Note that in blender, all that “parenting” really does, is it allows you to use the armature object as the root.
The issue could be you moved the object and didn’t apply transforms.
Also, you may not need to parent things (cloth for instance) you can just set the peoper armature in the modifiers tab of the object, and the mesh is usually exported with the correct skeleton - out of habit i usually patent stuff though, so i probably never tested this without proper parenting to the armature. You can give it a try still.
BTW, in blender the bone pivot location drives the transforms. if that’s what you are referring to that’s happening. Applying transforms helps, but you aren’t supposed to animate or mess with the armature when you do this.
Import it in engine and test how animations apply to it. IF they don’t work as you expect, then go with retargeting, which effectively takes care of shifting the pivot point translations.