As you have read, your mother would have been a Canadian citizen if her birth had been recorded by age two, but there were also other requirements contained in the original Citizenship Act that she likely did not meet. However, if she was a Canadian citizen when you were born, whether you have any claim to citizenship depends on your date of birth, which you haven't given. If before 1977 (and assuming your parents were married), then you would not have been a citizen by 2009, because you were born to a Canadian mother, not father. If after 1977, then you would have had to retain your citizenship by age 28. So, if you reached age 28 before 2009 and did not apply to retain your citizenship, then you are not a Canadian citizen.
As of April 17, 2009, your mother is a Canadian citizen, but because of the 1st generation limitation, you are not a citizen UNLESS you were already a Canadian citizen before that date.
I don't think the idea that your mother was "naturalized" makes sense in this situation (maybe the family meant a "natural born citizen"), but if she was a naturalized citizen, then you would be considered the first generation born abroad and you would be a Canadian citizen.
To sort all of this out, I would suggest that you submit an application for proof of citizenship, either for your mother or for yourself, and also apply at the same time for a search of citizenship records. The reason to apply for a search and proof at the same time is that then there is a single charge of $75. If you apply for a search and then later for proof, you would have to pay $75 for each. The reason you would give for the search is to establish a right to Canadian citizenship.
Just to be clear, though, if you are just trying to establish a right to citizenship for your mother, then you need no search. She is a citizen by descent and if she submits an application with her birth certificate and her father's birth certificate, she will receive a Certificate of Citizenship.