What you are looking to do is really not the intent of notebooks and you cannot pass complex data types between notebooks. You would need to persist your data frame from the child notebook so your parent notebook could retrieve the results after the child notebook completes.  This is inline with what @loui_wentzel recommended.

The better pattern here would be to take the logic in each of your child notebooks and create a function for each in a Python library that you could call from your main notebook.  After you have your function library, create a (.whl) file, install on the cluster, import the library into your main notebook and make the appropriate function call based upon your business requirements.