It sounds like her sensitivity is genetic. The problem with the younger generation is that their parents won’t allow them to deal with conflict directly. They intervene too soon and too harshly. I get wanting to protect your daughter, every father does, but, your daughter needs to learn to deal with conflict. 6 isn’t too young to be able to stand up for yourself. Tell her that the reason we fall down is so we can learn to pick ourselves back up. Tell her that we need to understand sadness to truly appreciate happiness. It will change her life