So sorry about your father's death.
I might not be as helpful as other people on this forum but Ill try to help.
Have you already sent in your application for a TRV? If yes, I believe you can send them a case specific enquiry, informing them of his passing away and request them for an expedited processing. Attach proof from the hospital/ funeral home and also let them know you will be returning to your country soon after your trip. Make sure your subject on the CSE mentions that its urgent. Send them an email as well.
I am not sure there is a specific process for an urgent visa for emergencies. I've been through something similar and time is of the essence. So email them asap.
