I have travelled a few times alone transborder with our daughter over the years. She has the same last name as me.

I have never been asked by the US official about a letter.

Most of the time, I have not been asked by the Canadian official about a letter. However, there have been 2 exceptions to this pattern. Once I had the notarized letter - no problems there. The second time I had a non-notarized letter from my wife; the Canadian customs official gave me a warning that a notarized letter is required, but she let us go.