Hey @maxsteiner  - 

I created a script within a business rule that will work - but I only used your example using the Watch List. You will need to generate more like what I have here, to copy more.

Here is the BR:
I have When to Run as Before, and I have Insert and Update equal to True

Script:

(function executeRule(current, previous /*null when async*/ ) {

    var gr = new GlideRecord("sn_hr_core_case");
    gr.addQuery("parent", current.sys_id);
    gr.query();

    while (gr.next()) {
        gr.watch_list = current.watch_list;
        gr.update();
    }

})(current, previous);

Parent Case: (These are all OOTB Demo Data loaded so no need to block out personal info)

Child Case(s):

When I add users to the Watch List of the Parent Case and Save/Update the record:

Here are the Child Case(s):

Everyone I added in the Parent case have been added to the Child Case(s).

Give this a try, and if you need additional help please let us know!

Cheers,

-Rob