I am so sorry you are facing such a heart wrenching decision.
My initial question is why is permanent custody at issue? Is it possible your parents could take your daughter with temporary gaurdianship? Are they near you where you could have as much time as humanly possible with her?
I guess where I am going with it is that permanent custody and removal from the home for her is traumatizing of course, but I wonder if making it a "temporary" arrangement or more like an extended visit with grandma and grandpa would soften the blow for both of you.
You are talking about the health and welfare of all your children. Each one requiring different therapeutic needs. Once those needs are met, you may find the reason for the separation in the first place becomes manageable and they can spend more time together.
The goal is just to make the next right decision. Let the master plan play out from there. If this is the healthy decision for them, then take a deep breathe and get it done.
Hugs to you.
Alice