The call centre agent advised you wrong cause you're mom should have chosen the "legally separated" status from the beginning. And your dad shouldn't be in the application. Since you already included him as non-accompanying you need to give cic more proof or evidence that your father doesn't want to comply.
https://www.canada.ca/content/dam/ircc/migration/ircc/english/resources/manuals/op/op02-eng.pdf
5.11. Inadmissibility and non-accompanying family members
All family members, whether accompanying the principal applicant or not, are required to be examined unless an officer decides otherwise. Normally, an inadmissible family member, whether accompanying or not, would render the principal applicant inadmissible.
There are, however, two exceptions to this rule described in R23. The first is the separated spouse of the applicant and the second is where a child of the applicant who is in the legal custody of someone.
Satisfactory documentary proof of a separation and of custody being with someone other than the applicant is required. A
separation agreement or custody papers
are examples of acceptable proof.
Officers will not issue a permanent resident visa to separated spouses, common-law partners or children in the custody of someone else,
even if they are examined. This is because
separated spouses and partners are not members of the family class as per R117(9)(c) and because children in the custody of someone else are non-accompanying family members.
Officers should be open to the possibility that a client may not be able to make a family member available for examination.
If an applicant has done everything in their power to have their family member examined but has failed to do so, and the officer is satisfied that they are aware of the consequences of this (i.e., no future sponsorship possible), then
a refusal of their application for non-compliance would not be appropriate.
https://www.canadavisa.com/canada-immigration-discussion-board/threads/individual-pr-spouse-not-divorced-and-not-living-with-spouse.478048/#post-5898163
(read post #6)