Joseph Smith and the Priesthood, By jay A. Parry illustrated by Jerry Harston, Liahona Publisher, Salt Lake City, Utah, 1979.
This is an interesting book, geared for children, about the restoration of the priesthood. It tells the story of the restoration of the Aaronic Priesthood very succinctly. It tells a story with regards to the restoration of the Melchizedek priesthood which I had never heard before. It tells that Oliver and Joseph were running away from a mob intent on taking their lives and putting an end to the new religion. The fled into a wood, which became very dark. the struggled all night. As the sun was coming up the next day, Oliver asked Joseph how long would there be persecutions. At this moment a light appeared and Peter James and John who restored the Melchizedek Priesthood and called Oliver and Joseph as apostles.
As I had never heard this story, and this is a children's book, I wondered if it could be true. The story is attributed to Brother Addison Everett. He said it was told to him by Joseph Smith shortly before the martyrdom. However he did not relate the story until some 38 years later, and then he was in his seventies. So this is a witnessed account, but the reliability of the witness may be in question.
This article linked from lds.org spends considerable time discussing the date of the restoration. It concludes it had to take place between 16 May and 29 May 1829; the day after the restoration of the Aaronic Priesthood until Joseph and Oliver left the Susquehanna area due to persecution.