If there was somehow a mistake, and you do want your child in first, I'd act like my child was entering first when you call to check on that letter.

When I miraculously was accepted into an architecture program without submitting a portfolio (i was in pre-arch at the time), I received a letter from the university saying "we made a mistake and we need you to sign this form to fix it"). At the time, I had already switched majors, again, but there was no way I was signing that!