The title and first sentence of your post really have almost nothing to do with your actual question, and it doesn't really make sense to me to use a checkbox instead of a button for this purpose. Having a checkbox that says "No Show" and deleting the entire group instead of hiding it is misleading.
Nonetheless, if you were to use a checkbox, and the checkbox's field were a child of my:group2, the code would be something like this:
if
(e.NewValue == "true")
{
XPathNavigator group2 = e.Site.SelectSingleNode("..", NamespaceManager);
string myNamespace = NamespaceManager.LookupNamespace("my");
while (group2.MoveToChild("group3", myNamespace))
{
group2.DeleteSelf();
}
}