@mary - maren's code looks mostly right. maybe the conditionals are off. i'd use her code and amend the bottom functions to
function child_1st_subsidiary_aside {
if (is_active_sidebar('primary-aside') && is_home()) {
echo thematic_before_widget_area('primary-aside');
dynamic_sidebar('primary-aside');
echo thematic_after_widget_area('primary-aside');
}
}
function child_2nd_subsidiary_aside {
if (is_active_sidebar('secondary-aside') && !is_home()) {
echo thematic_before_widget_area('secondary-aside');
dynamic_sidebar('secondary-aside');
echo thematic_after_widget_area('secondary-aside');
}
}
check the codex for info on WP conditionals
http://codex.wordpress.org/Conditional_Tags