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You need to unparent, then move the parent layer.
The good news: you can select all the child layers and select None from the drop-down menu. It's just as easy to select all the child layers and parent them all at once, too.
I realise this is a relatively old post, but as this has just come up on another list, I thought I'd post this suggestion. It might be easier if you have a complex comp and can't simply 'select all' the child layers
1. Add a new null to your scene in the position you you want the parent null to move to. Call this null 'NewParent'.
2. Parent your current parent to 'NewParent'.
3. Delete the old parent.
Your other layers should now be children of NewParent.
Thanks for the tip!
(It's really cool in Cinema 4D — just hold down the "7" key on the number pad and you can move a parent without disturbing the children. Incredibly handy!)