Edit button displayed, although user has no permission to edit the referenced node

I am trying to find the right setup for following usecase:

Authenticated users (or other roles) are allowed to add new child nodes, but not to edit or delete existing child nodes.
So I checked the permissions on people/permissions :
Allowed to see add and edit buttons checked
Certain Content Type (Child nodes): Create new Content checked (all other edit any/own and delete not checked)

If a user with this role go to node add/edit parent form, both buttons (edit and add) are shown although the user has no permission to edit child nodes.
If the user click the edit button (pencil) the form is closed and a "Access denied" message is shown. The user has to find the "Browser Back Button" to return to the form.

What I expect or suggest:

Disable or hide the edit button, if the user has no permission to edit child nodes
or
Dont close the form and show a message on top of the form, that the user is not allowed to edit child nodes.