"You need to eat something other than bagels and chicken fingers," his dad said.
"You know what I can do?" added mom. "I can make a fruit smoothie really quickly."
Sunday's snack tally: 635 calories for Andrew and 390 for Liam.
Registered dietitian Samantha Heller said, "If I had to give the Tullys a grade, it would probably be a C."
"They are eating over half their recommended calories for their age in salty sugary snacks," Heller said. "Even though their kitchen is full of healthy snacks, the kids are loading up on sweets."
Heller says there are things parents can do to limit snacking.
Don't let your children snack out of habit. Make sure they are actually hungry.
"If you're snacking just after dinner, you're not hungry," Heller said. "They just feel like eating, and it's fun."
Put your money where your mouth is.
"You can't have a parent eating doughnut holes and telling your kid to eat carrots," Heller said. "That won't work."
Stop stocking your kitchen with bad snacks.
"When it's yogurt, chocolate pudding or apples, who is going to win?"Heller asked. "Well, the chocolate pudding will always win out every time. So A, I wouldn't give the child a choice, and B, I don't think I would have the pudding or the cookies in the house."
Take away the unhealthy temptations, Heller says, and kids will embrace the healthy ones.
ABC News Lara Salahi contributed to this report.