Cover your .... You can write the letter yourself and usually find someone who will notarize it for free if you already do other business with them.
I would guess that having the same last name would be seen as a GREATER risk factor than the last names not matching. Most kidnappings are done by a parent because he/she doesn't have the other parent's consent. I was turned away with my own daughters at the border way back in 1996 without a letter from my wife, and I can't imagine they've gotten any more lenient.
My 15-yo was questioned in Nov. crossing with my wife, and she even had a notarized letter from me. My advice in this case is NEVER answer for the child. Just hand over the paperwork, let the officer do her job, and you should be fine.