Complex sentence: After a brief but violent battle which killed between 500 and 1000 and left around 20,000 homeless, the Binh Xuyen were crushed and Diem regained US confidence and control of the police.
Split into simpler sentences: After a brief but violent battle that killed between 500 and 1000 people and left around 20,000 homeless, the Binh Xuyen were crushed. Diem had regained both US confidence and control of the police.