You can add the contents of the pop-up on the page wherever you need it and set a visibility condition to it.
Set this boolean to true when the user clicks on the modify button.
Is this what you want to achieve?
There is new question, how can we click the edit button on the left to display the PublicItem list
associated with PublicParameter on the right, with a layout that looks like this, instead of a Parent-child container?
Similarly for this you can set a visibility condition to the listview,
Set a boolean to true when the user clicks on the edit button.
But you will have to enclose this listview in a dataview with PublicParameter object because you want to show all associated objects in it.