Accessing other users files

Simply put, you can't from the finder.

Actually, that's not true .
You can edit the permissions through the Get Info panel on each folder, forcing everyone to have read/Write privileges to the folder and contents. What I'm not sure about is how the permissions from your child's account will react to the changed files and new files you ad within their home directory.

 

I do this on Macs I have responsibility for. It saves having to switch users as often.

Get Info on the folder & give yourself read & write access. Click the gear & apply to all enclosed items. I do find that you sometimes have to repeat the process with some buried folders.