Read Genesis 16 to 18. What would be the promised child's role in relationship to God's covenant?

Frustrated and probably bewildered at their childlessness in the face of God's promise, Abram and Sarai (newly named Abraham and Sarah) take things into their own hands.  In Genesis 16, they produce as heir (Ishmael) for Abraham through Sarai's maid Hagar.  What astonishing promise did God give them in Genesis 17:15-22 and 18:1-5, and what would be the promised child's role in relationship to God's covenant promises?