I agree with both answers so far. You were not in the wrong on your position. but the way you addressed it was not right in my opinion. My opinion though has very strong family relations, and my relationship with my brother and sister in laws are very important to me. So...you were right about it being your house, your rules, and you were being safe with your firearms, and she has no say in that. You were wrong that you let an opportunity go to show your children how to be better than your opponent, and to help educate an "educated" person.
“One of the illusions of life is that the present hour is not the critical, decisive one.” – Ralph Waldo Emerson