From Paul Brians’ excellent book Common Errors in English Usage (which you can access for free by clicking on that hyperlink), here is a worksheet on the use of in spite of and despite in prose. This is a full-page worksheet with a reading to drive some extemporaneous writing using these two prepositions.
If you find typos in this document, I would appreciate a notification. And, as always, if you find this material useful in your practice, I would be grateful to hear what you think of it. I seek your peer review.
Mark's Text Terminal 