Sorry to hear about the loss!
I will suggest you to write an explanation letter and explain the whole situation in it. Mention that you birth certificate only has your father's name, but to prove your relationship with your mother, you can provide copy of your passport and education documents which carry the name of your mother. Also mention about your father's death in the letter, provide date and place of death.
Make sure your put your Name, UCI, and the DOB in the letter and sign it. After printing and signing, put this letter right after the first document (ITA Letter provided by IRCC).
You are still required to provide a certified translation of your birth certificate.
I will also recommend you to go though the guide on the following link, it will help you in preparing the application package:
https://www.canadavisa.com/canada-immigration-discussion-board/threads/a-guide-for-preparing-parents-sponsorship-immigration-application.569846/page-4#post-7845935
I will pray for your Mom's application, good luck!