Her only child, 21-year-old Brandon Sapp, was killed in 2004 in Iraq when the tank he was driving backed over an explosive device.
She said the public is entitled to see images of caskets if a family approves.
"Every family grieves differently," Veverka told ABCNews.com. "Some can't even talk about it and others like me want it open. For me, I want to show the world what happened to my son."
But she said the slow military process is grueling on grieving families and the press doesn't make it easier. News travels fast in communities, and arriving caskets can easily be identified when deaths have been announced.
If the ban is lifted, Veverka wants the military to take "extra measures" to ensure privacy for those who want it.
"Before they even arrive at Dover, a lot has happened to the families," she said. "The military has shown up at my door and told me. I am mortified. I am sobbing on the floor. At this point my son is still in Iraq or they have flown him to Germany."
"You sit in a nightmare and your heart is wrenching," said Veverka. "It almost broke me, and I'm a pretty strong woman."
Families cannot even make funeral plans until the body is returned to U.S. soil.
"The sad part is I'll never get to hear 'Mom' again," she said. "I still turn in stores when I hear it. This is the reality of war, not 'Let's all go in and kick their asses.' Men and women die over there, on both sides. It affects everybody.
"It's a ripple effect," she said. "His life touched this person and they let me know, then my friends, then the community and to the media. I call this the ripple effect of dying. Imagine when 4,200 men and women have died. Part of that is showing what happened to my son."