I figured it out

"An-yee" means "Candy"!! The mystery word is solved. Tonight Violet asked for a piece of candy. I told her she could have one piece after dinner, and she didn't let me forget. So after supper she went over to the storage closet where she knows some candy is and asked for the piece. Calvin ran over and stood with her, and shouted "an-yee! an-yee!" as she was saying "candy! candy!" Each kid got one starburst chewy. :) At least I know. A few days ago he was pointing at that closet saying "an-yee" and I didn't have a clue what he meant. He is learning a few more words: Bubble, apple, Aldi, oatmeal, and poon (spoon).