Agreed. Even if this was a long-standing family tradition, it's clear that not everyone follows it. Mother would, even in the best interpretation, have been much more gracious to have said, "Dear, may the rest of us share your cheesesticks?" That would have clarified that the child was in agreement as to the disposition of said refreshments. Even better, it would have encouraged the child to remember to offer for herself next time.
Even (especially?) in a family, basic courtesies, such as asking permission to take anything that can be referred to as "yours", should be followed.