How can I schedule change of the default front page? I have a node being displayed on the front page, set at admin/config/system/site-information > Frontpage.

I need to change it to another node on specific date.

It would be ideal if I could do that using views display of /frontpage + Promote node to frontpage. But i have a referenced by nid view inserted into the nodes of this content type (using Views Field) which does not show anymore if I use this method.

Thanks
I would add a date field to the node and then filter the view to only show the node scheduled for today. Point your front page to that view.

You'll need the date module.