I do both... FIRST, I do it when my kids are not home and get things weeded out that way.
I do NOT rearrange everything... just weed through it then toss.
THEN... they don't really notice it.
THEN, for the minor stuff... I ask them their opinion on it.
MOST times, my kids don't even know I tossed things out.
Last summer, I tossed 18 garbage bags full of stuff.
My daughter, NEVER even noticed nor missed, what I threw out.
I also tell my daughter (she is the clutter kid in my family), that BUGS will come, if we don't clean it out every so often. So this rationale, works with her....
BUT... the KEY thing is: you HAVE TO know, what is truly special to her and irreplaceable or a family heirloom etc.... and if it is from her other Mom or not. DO NOT throw those things out.... or it will really, cause hurt.
I for example, have a special plastic box, just for those things. Only. And I label it so no one will throw it away. In it are even a few things that I gave my daughter, from my own childhood.
Good luck,
Susan