While US-Canadian couple get approved very quickly on a common law application, you have enough evidences to apply as a common law partner. As others suggested if you get married, it will be smooth journey for you with no headache!canadianwoman said:You can use the letter, since she had it notarized. It is unlikely the visa officer would contact her. If she contacts them, then they would look into it, but as the letter is notarized, and you have other proof, it might be enough.
Without the letter you do not have enough evidence for common-law, in my opinion. You have to prove that you lived together for 12 continuous months, and that the relationship is genuine. The hotel receipt helps to show genuineness. The joint account and the phone bill do not cover 12 months. The notarized letter from your mom, and the Statutory Declaration of Common-Law Union are good, but will not be enough by themselves to prove common-law. If you have government mail from each month before you have a shared lease, then that might be enough. If not, it is good extra proof, but not enough.
Honestly, I would just get married. All the evidence you have is good for showing your relationship is genuine, and in the application you should state that you have been living together since the time you moved into his mother's house, but if you are married this then becomes extra proof, not something that is essential.
However, if you decide to go with common-law, and use the mother's letter, you do not have to explain the situation with her. Submitting the notarized letter along with the other evidence of common-law would be fine: she did not lie in the notarized letter, and you do not have to tell the visa officer that your relationship with her has soured (unless asked specifically, of course).
Hasan