Showing just children categories of the parent category I’m in

To stop my navigation getting out of control, I want the sidebar to show all parent categories, but just the children categories of the parent category that I’m in. And I want the current child category I’m in and its parent category to be highlighted.
So sort of like this for a post that was in child category 3 of parent category 2:

• Parent 1
• Parent 2

• Child 1
• Child 2
• Child 3
• Child 4

• Parent 3

I know very little about PHP, so I’ve tried copying and pasting bits of it and amending it but I can’t get it to work. A couple of widgets I’ve tried don’t work either.

Anyone got any bright ideas? Thanks a lot!