How can I perform an inline editing inside a nested admin?

In your code you are using delete which is not a valid option. Maybe you can try 'btn_delete' => falseCheck the documentation for all the valid options here.

If this not working, maybe sonata_type_collection is the solution to your problem. Ensure that you are using the by_reference option the correct way depending on your relation.

Try this in the form mapper :

  $formMapper          ->add('title', 'sonata_type_model_list', array(                    'class' => 'YourBundle:String',                    'required' => false,                    'delete' => false,                     'btn_add' =>true,                ), array(                    'edit' => 'inline',                    'inline' => 'table',                ))            ;

If the error persist try to get a look at the Doctrine2 documentation :Doctrine2 One to One association mapping and then generate your entities

You said that chrome console gives you error:

Call to a member function getName() on a non-object

So this error is not from javascript?

If error from PHP it means that when you try $object->getName() (it must by in OSC\UtilsBundle\Controller use Ctr+f "getName()" in file editor to find that line) $object is not an object, that can by because you maybe get obeject array, not single object. Try add var_dump($object); and you see what is it.