I might agree with your mom. If you let the dog eat at the table, only do it when everybody is done. But letting the dog eat off of your fork and then going back to eating with the same fork? I wouldn't be able to continue eating at the table...yech!
Not utensils (they had their own, believe it or not) but dishes and bowls. Usually the dinner plates were off limits however.
My dad always had a "pet" peeve of not letting our dogs near the table at meals. Incredibly the dogs knew they had to hide under the table near one of the rest of us and that would work. However now that my parents have a pet that they're around 24/7 since they've retired, he gets away with murder. His cat-condo is in the dining room and when he sits on it my dad feeds him occasionally. When he does he gets a chorus of "HEY DAD NO FEEDING THE CAT AT TABLE!"