Without setting up similar tables and testing it, this would be my first guess:
select customer.name,sum(summary.total)
from customer,summary
where customer.cust_id = summary.cust_id
and summary.inv_num = detail.inv_num
and customer.bill_st = "GA"
and summary.shp_date >= (date() - 365)
and summary.inv_num not in
(select detail.inv_num from detail where substr(detail.inv_id,1,2)="SE")
group by customer.name
having sum(summary.total) > 1000

My apologies for wasting your time if it doesn't work or at least get you close.