Thanks for your response.
I went on VFS website and booked the passport submission. I received one email appointment confirmation for each application. The email specifies that the name on the letter should match the name on email confirmation.
Now my mother's name is not present on the CIC letter. I called the VFS agent in India. The agent told me that the letter should have both the applicant names or else they cannot accept the passport. May be the agent was not completely aware of the situation.
Should go ahead and submit the passport at VFS and see what they have to say?