Partitioning does not partition data like on a hard disk, it allows you to create different views of the same objects for different users. Where a PM can only see their own projects, this will be a security related issue, not a partitioning related issue.
There are may ways to approach this, and I would first take a look at your security model as I hate the maintenance around instance rights. Automate if you can, We have.
based on your requirements above, I believe that you would require the following instance right to the Child project:
project - view: This allows you to view the general, financial, custom defined fields, tasks, processes, and sub-projects for that project.
I have not tested and I am only going from the top of my head.