John Van Seters believes that J used Deuteronomy as a source, not vice versa. Why? On page 310 of Life of Moses, he gives one reason. He looks at J’s story of the Golden Calf in Exodus 32. (Van Seters attributes it to J, whereas others have treated it as E’s polemic against Jeroboam’s golden bulls.) Joshua is in J’s story. But Joshua is absent from Deuteronomy’s telling of the Golden Calf story. Van Seters states:
“It is more surprising that Joshua, a major figure in DtrH, should be ignored if he were present in the account before D. Joshua’s role in the story is, in fact, another of J’s embellishments of the account.”
For Van Seters, if D were using J as a source, then D’s version of the Golden Calf story would include Joshua, for Joshua is in J’s story, plus DtrH loves Joshua. But D does not mention Joshua, and so there is a greater likelihood that J expanded on the D version and put Joshua in.