CiviEvent link Parents with Child participants during registration
I dont think registering for an event and creating a relationship using the standard CiviCRM event registration pages. 

So if you use CiviCRM with Drupal I would go for the webform solution. 

There is also a third possibility and that one is using the form processor extension in CiviCRM and then use the CiviMRF to submit you the webform data to CiviCRM. I wrote an example instruction in this blog post: https://civicrm.org/blog/jaapjansma/using-civicrm-form-processor-extension-to-handle-form-submissions-from-an-external

The pro of the form processor solution is that you can create a webform on a remote website. Or in other words, if your website and crm are not on the same site this solution will also works. The con is that it requires a bit more knowledge to set it up.