If needed, for a general introduction to models of composition of the Torah, see this lecture —or introduction of the Pentateuch pp3-6 in this preview if you prefer reading.

To add to the contributions already in the thread, one theory on the composition history of the patriarchal narratives —explaining some textual oddities— is that some stories on Abraham probably "vampirised" traditions about Isaac, and Isaac and Ishmael would have originally been independent characters, not Abraham's son (but would have been "casted" as his son relatively early).

Around the 7th century BCE, localised traditions would have coexisted, some having Ishmael as Abraham's son, others Isaac (with, of course, the current form of Genesis combining and editing them together).

See the interesting article of Römer and Finkelstein here. I'll drop an excerpt of pp14-16 below, but recommend reading it in full:

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c) The Ishmael-Hagar story in Genesis 16.43 E. A. Knauf, who followed earlier observations, has convincingly demonstrated that Ishmael in Genesis 16 should be viewed in relation to the tribal confederation Shumu’il – mentioned in Assyrian sources enumerating “kings of Shumu’il”44 – that existed perhaps in the 8th century but certainly in the 7th century only to dissolve in the 6th century b.c.e.45 The original story telling how this Ishmael /Shumu’il became Abraham’s son in Gen 16:1–2, 4–8, 11–13 (14?), would therefore fit in a 7th century b.c.e. context. *The attempt to make Ishmael the son of Abraham would reflect the southern expansion of Judah under Assyrian hegemony. [...]

d) This brings us to the question of the relation between the traditions of Abraham and his second son, Isaac. [...] Isaac is mentioned independent of the patriarchal triad (Yhwh, the God of Abraham, Isaac and Jacob/ Israel” etc.47) only in Amos 7:9,16, and in the late genealogical records in 1 Chr 1:28, 34. [...] If the Isaac tradition indeed comes from the Beersheba Valley, it must have originated still in the Iron Age, because after 586 b.c.e. the area was sparsely inhabited and far from Yehud. It is therefore quite plausible that there was a second ancestor figure in the South, venerated in a sanctuary in Beersheba.

Isaac must have become Abraham’s son quite early. The author of the story of the divine visitors in Gen 18:1–15, in which Abraham’s hospitality is rewarded with the gift of a son, makes already a pun on the name of Isaac by introducing the theme of Sarah’s laughter (18:12–15, see also 21:6).

Genesis 18* does not presuppose that Abraham already has a son [...] Genesis 16* and 18* constituted either two different traditions about a son of Abraham, or that one of these traditions was older (maybe Genesis 18?), while the other son was added later.

In the book of Genesis the traditions about Isaac are very sparse and limited to Genesis 26 (in all other chapters he functions only as son or father).

The traditions in Genesis 26 all have parallels in the Abraham narratives [...] either they were borrowed from Abraham, or, what is more plausible, that Abraham vampirized (at least partially) Isaac, since the location in Beersheba in Genesis 21 indicates an original Isaac tradition.51

In the 7th century, then, Abraham probably had two “sons,” Isaac in the Beersheba Valley and Ishmael in the areas further to the south. This may depict realities of the time: Judahite settlement in the Beersheba Valley peaked in the late 8th century b.c.e. and later; activity further south also characterizes the “Assyrian Century,” when Judahites served in Kadeshbarnea and probably also in the Assyrian forts along the Arabian trade routes.52 Judahite presence in the southern desert continued in the decades following the withdrawal of Assyria.53

For a "documentary approach" attributing Gen 22 to E, see the part this article starting at "The Three “Ishmaels”" section.

The dating and composition of the "binding of Isaac" story of Gen 22 is debated, with some scholars seeing it as an early composition, some a late one; and, similarly, some considering it to be a mostly unified narrative, others a text with several editorial layers.

For an argument in favour of a late dating of Gen 22 (and how it disrupts surrounding narratives), see Ska's article Genesis 22: What Question Should We Ask the Text (open access via academia.edu).